Mainly the Spanish went where there were "cities of gold" to conquer, leaving territories that lacked such attractive features pretty fallow.
Certainly the Spanish claimed the entire Western hemisphere.
Insofar as we can ATL in some major urban development and some degree of precious metal wealth, we can have the Spanish attracted to conquer it, and subsequently use the surviving conquered population to support their Peninsulare ruling classes and "Criollo" persons of Spanish blood born outside Castile.
North of the Carolinas though I am not much aware of major precious metal deposits on the northern Atlantic coast.
As others note, the more distant they get from their other settlements in the Caribbean and MesoAmerica and the "Spanish Main" northern coast of South America, the more marginal and at risk a northern settlement is. I suppose the Spanish can adapt to the Atlantic coast climates, though New England winters would hardly be attractive.
In view of how important gold or at least the rumor of gold is in attracting conquistador attention and sustaining efforts, we might basically have to do an ASB geographic POlD cheat and invent ATL metal deposits, or some other precious attraction (diamond fields or something like that).
Or go for a bio-agricultural POD, and make it a twofer--postulate, a la Jared's Lands of Red and Gold, development of some highly useful crop variant that centers in the north. We don't have to go so far as DValdron's Lands of Ice and Mice and locate it in the actual tundra--though asking and answering this question in the frame of that particular worked-up TL might be interesting! Indeed Spain and Portugal were shown, in a 17th century context IIRC, in the preview opening post (by DirtyCommie, the technical thread owner) to be attempting to be involved in trade with a "Thule" society more or less based in parts of Canada of OTL.
But here we seem to be talking about Georgia to Nova Scotia and not beyond, so take a different bio-POD. OTL Native American people developed a great many crops so it is not even ASB levels of implausible; it is quite reasonable to suppose some crop type flourishing in the more northerly Atlantic coastal zones, perhaps originating in the Great Lakes region actually, might lay foundations for as deep, ancient, widespread and diverse a civilization zone as the entire sweep of MesoAmerica.
Anyway, include in the crop package something that is to tobacco or chocolate what gold or silver are to tin or copper--some kind of drug perhaps, say a fungus or a flower or fruit that has psychoactive effects that European society comes to value highly.
Another good trick is to scout out any OTL known gold or silver deposits anywhere in the broader Great Lakes region, and postulate a major civ complex there (without a wonder drug) and wherever we want on the Atlantic coast--Massachusetts Bay, Hudson mouth, Chesapeake--has another civilization complex,perhaps a colony of the midwestern one or a hybrid of its agriculture and general culture with the advancing "three Sisters" MesoAmerican one, which is rich and powerful enough to have acquired a great deal of the precious metal in circulation over many thousands of years. Say the site of OTL Richmond (or Civil War buffs might point out a fantastic location combining both fortifiable defense assets and access to the river/bay system) is the "Mexico City" of a region covering essentially all of Tidewater Virginia and Maryland with a great many 'cities of gold.'
To make it more challenging for the Spanish, move it to say Hudson river valley and make Long Island and Manhattan the major centers of the coastal outpost that attracts them--or heck, put it all the way up the Saint Lawrence around where Quebec city and Montreal are. If the Cities of Gold are attractive enough they'd try to conquer Greenland I suppose.
It is worth noting the successful ventures of the non-Spanish were mostly far north out of reach of the Gulf of Mexico/Caribbean bases of earlier Spanish power--but also that they were of much much later vintage too. Newfoundland I believe was claimed by the English crown pretty early on, but amazingly the Newfie colony did not branch southward to Nova Scotia or up the St Lawrence until the French preempted them, and did not reach down past Maine to Massachusetts or the Chesapeake either, for another hundred years, in ventures that bypassed Newfoundland completely. The kings of both England and France protested the Treaty of Tordesillas and that they were not consulted or considered, and denied the right of the Pope to limit them. But they didn't do much to make good on these bold and angry words; even as late as Elizabeth's later reign when the Armada had been defeated and the ascendency of England was well under way, there were no successful mainland colonies (bearing in mind that Newfoundland is an island, and that the ventures of Bermuda and Barbadoes were also far offshore, this was strictly true). Roanoke was attempted but failed; only under her successor James was the first English colony on the North American mainland that would survive launched. Meanwhile early French beginnings in the Saint Lawrence region antedated 1600 I believe, but not by a lot.
The Spanish had free rein to take anything they wanted on the North American coast beyond Florida, and to an extent as noted did so--but gave up for reasons given upthread. It is most reasonable to conclude they just weren't much motivated and were focused on gold, silver and taking over semiurbanized civilization centers already in being.
I don't think all the options I suggested above are equally ASB; certainly geologic PODs siting precious metals in places not found OTL are only ASB by technical decree. Vice versa, as others noted, Georgia area gold was right there, but unknown to the Spanish, who relied on Native American civilization builders to dig it up and work it and display it for them to plunder conveniently, and guide them to the mines. It would not be ASB in the least for the Spanish to learn of this gold, but lacking the extensive degree of civilized warring city states Mesoamerica had, one has to wonder if even the gold-hungry Spanish would have though it cost effective to go to the trouble of securing what amounted to their eyes to a primitive wilderness in the off hope of finding possibly rich, possible marginal, deposits they would have to import workers of some kind to dig up and build the infrastructure to bring it to the coastal ports.
Having ATL heavily developed city-state systems a la MesoAmerica or even a vast unified empire as in the Andes far north of the tropics would have been entirely possible, and of course to a limited extent it did happen in the Mississippi-Ohio river valleys. Alternate crops are a realistic POD, but pretty chancy; one has to have a good knowledge of botany to pick out candidates with possibilities offering marked advantages over the wide variety of cultivars Native Americans did develop, and in some cases abandon, OTL.
Anyway to lure the Spanish far north of Florida one would need some spectacular cities of gold I think, and if they were situated too far north, it is possible the disgruntled French and English monarchs might have put more money where their mouths were and tried to preempt the Spanish there. I am not sure early Tudor England had the manpower required to subjugate a Saint-Lawrence River mouth outpost of a Great Lakes civilization complex. If Henry VII or VIII could pull it off (which attempt would put the kibosh on a lot of the younger king's maneuvering, such as dynastic links to the Spanish crown--unless he were to negotiate a franchise with the Spanish as it were) I wonder to what degree the English would mimic the Spanish approach to governance and to what degree they would hit upon quite different political solutions.
Anyway that is going way off track and doubly, letting some other royal system than the Spanish have anything, and getting away from the Atlantic coastal strip of 13 colonies in favor of pushing inland to the Great Lakes/Midwest.
I think realistically, Georgia as an extension of Florida northwestward to encompass the highland gold fields is about as far as Spain would like to reach. If they do mine a fair amount of gold and develop the coastal port areas (around Savannah I guess) they might put more effort into missionizing northward to secure their flank, which I suppose would peter out around the South Carolina/North Carolina border. Basically then this maximal Empire of the Indies, El Norte branch, would preempt 2 of the 13 colonies but probably not do much to stop the English from claiming and securing at least North Carolina, which I guess would just be called "Carolina" full stop. Beyond that North America could develop as OTL pretty much.
Now a question arises--if the Spanish were mining Cherokee Appalachian highland gold starting in say 1570, but by 100 years later would be too weak in the region to contest the settlement of "Carolina" (NC, recall), would the British, who got into the ascendency over the entire Spanish empire in America in terms of trade concessions, pressure Spain into ceding Florida Norte outright, and perhaps with it all Florida? (If the Spanish had developed major settlements in the southern Florida peninsula it might make sense to leave them the tip as part of the defenses of Cuba, but as far as I know they did very little in that respect, most of their effort going to Saint Augustine and to missions in the Tallahassee area and to Pensacola). Or would the British, in the waltz of shifting alliances, leave the Spanish claim alone and just focus on sewing up its trade concessions?
As noted, I expect Spanish reach to be limited in intensity and commitment, OTL the British got around to seizing Florida in the same war mainly against France that led to the French monarchy conceding its territories in North America to Britain, or to Spain. Then the ARW led to Britain giving Florida back to Spain, where the Americans then whittled away it at until Spain was made an offer they could not refuse to purchase Florida.
Thus even if the UK finds it politic to concede Spanish control all the way up to the OTL North Carolina/South Carolina border going into the 1750s my guess is Spain then loses control and cedes all of the northeast mainland claims to Britain sooner or later, and it would be after both French and Spanish threats to the coastal colonies have been exorcised that the American colonists might get feisty and patriotic as they deemed it, or quarrelsome greedy and rebellious as the British authorities saw it.
The upshot would be much like OTL California or Texas I suppose--to this day major elements of California common law stem from Spanish common law.
However the more I think of it, even if the map shows a sweeping British domain of everything east of the Mississippi much as OTL, if the Spanish march which I believe they'd just name as part of greater Florida comprising OTL South Carolina and Georgia were only to be brought under British rule by around 1763, its British settlement would be not much underway around the time of the American revolutionary crisis, even assuming it develops on a timeline very similar to OTL. The territory south of OTL North Carolina would be but sparsely settled, and its new British colonists would at this early date have little in common with the older 11 colonies to the north, and thus I suppose would tend to fall under Loyalist domination. Assuming the US rebellion can prevail at all in such circumstances I'd think that we'd basically wind up with a two-Canadas situation, with Southern Loyalists from Carolina and Virginia and Maryland and so forth fleeing south--perhaps a great percentage of those who fled north to OTL Canada would go south too, slowing the Anglicization of the northern loyal colonies (but these territories would be about as secure a British holding as OTL, due largely to the conciliatory nature of British rule over their "Quebec" Francophone subjects. Meanwhile the young USA is between two British fires as the Loyalists who go south would cause a surge in Anglo population of "the Floridas"--Britain seems liable to administratively divvy the swathe of territory generically known as Florida but the pieces would retain the name I think, much as OTL.
I envision three Floridas, under Spanish and then British rule--somewhat to the north of St Augustine, a new ATL or expanded forgotten OTL Spanish town probably around Savannah I guess becomes the capital of Florida Norte or Alta Florida, which comprises OTL SC, and northern Georgia reaching into Alabama, basically the mountains where the gold is to be found and rivers flowing southeast to the coast; some such stream defines the boundary with older east Florida which reaches west to the region of Tallahassee and Apalachicola Bay, and a West Florida centered on Pensacola and Mobile reaching to the Louisiana (Spanish territory, after 1763) border, and northward inland a considerable distance.
Alta Florida would be most intensively settled first by Loyalists, and thus pole-vault toward comparable demographics with the corresponding US states of OTL. As such it is an existential threat to Carolina; perhaps instead of an OTL Constitution of 1786, the Articles of Confederation are amended piecemeal to better enable the new US Federal government (a super-parliamentary type system dependent on the majority factions in the Continental Congress, where the CC creates committees to oversee particular executive functions carried out by CC appointed executive officers serving at the CC's pleasure) with key amendments needed initially to reinforce and systemize the CC's power to collect taxes from the states, and authorization of a standing Continental Army, whose major preoccupation would be securing the Carolina-Alta Florida border.
Behind this shield of disgruntled dislocated Loyalists, the two southern Floridas would develop at leisure. I don't see the USA being in a position to pick fights with the British (yet we did OTL, hopefully either we have the wisdom not to, or can survive an ATL version of the War of 1812 about as well as OTL overall) and certainly not pick fights and win, nor does Britain have any motive to sell any of this vast expanse of "Floridas" comprising the lion's share of OTL Dixie.
It would be interesting indeed to see whether the economic opportunity to develop the Floridas as cotton plantation zones would delay British Empire wide Abolition, or change the terms of it much. Inheriting Spanish common law, the late Spanish Empire rather frowned on slavery and tended to assert slaves had rights in a way alien to the more brutal British system of slavery, but I suppose initially such qualms would be shoved aside by the new British regime, and especially by the dislocated Loyalists. Against this powerful and growing pro-slavery lobby, the Loyalists will have defined themselves in large part by their deference to London as the center of the system they support, and the various interests that promoted abolition of slavery in British dominions would I think prevail over any combination of colonial lobbies. But the latter might be able to delay it or change some of the detailed terms, perhaps.
Denied slavery after say 1830, I am not sure what expedients profit-minded plantation entrepreneurs in the British Floridas would hit upon, but OTL British Empire history points to a spectrum of institutions many of which were almost tantamount to slavery, and I suppose some eclectic mix of peonage of nominally freed former slave populations, and indenturing "coolies" from British Asian holdings, along with attempts to compete on a wage paying basis (which would be generally doomed unless it favors a format of collective-cooperative worker-owned operations, that might also be an outlet for Utopianism, and also these sorts of ventures would tend to invent lots of labor-saving gadgetry) would enable the region to roughly replicate OTL plantations and feed the demand for raw cotton in British and other European industrializing nations, and perhaps even by this later date the USA.
Meanwhile north of the border, quite a few slave states remain, but their number is severely limited--Carolina, Virginia, Maryland, Delaware; the former two can probably much as OTL spin off new states of Tennessee and Kentucky but that would be the limit, 6 out of 13, meanwhile the northwest frontier offers scope for such states as Ohio, Indiana, eventually Illinois and Michigan and Wisconsin--note Missouri would require crossing the Mississippi and the leverage and opportunity and domestic pressure to seize those lands are all truncated. A pressure to try to get some corridor to the Pacific would exist but it is hard to see a path.
The slave states are thus outnumbered from the get-go, yet were foundational in forming the USA, so especially in context of abolition prevailing in British dominions, I suppose the USA would follow a path of gradual emancipation, with the slave states themselves drafting the legislation. US slave owners would lack the windfall opportunities of cotton plantations.
Meanwhile I think such a USA would undergo democratization much as OTL. Initially all states have equal representation in the Continental Congress, but in the context of enforced taxation (levied on the state governments, not on US citizens as such) I note that the provision in the Articles was for the CC to assess the overall wealth of each state and ask for taxes in proportion; now that taxes are being assessed and demanded, not asked for, the states will possibly come round to making power in the body proportional to the tax bill, specifying numbers of representatives from each state in proportion, and permitting individual members to vote as opposed to the former practice of states voting as one bloc. (Given the way the Articles were written, with lots of specified supermajorities for specific types of actions, I suppose in some cases states would still vote as blocs). Originally, the delegates to the Congress were handpicked by the various state governments, but I suspect over time, as democratic principles assert themselves, various states will start either permitting voters to elect the delegates directly, or adopt rules permitting the factions in the state legislature to claim proportional shares of the state's total delegation. Thus the CC will evolve from a coordinating committee between state governments to a US national representative body where partisan allegiance is more important practically most of the time than what state a delegate is from.