Mexico is doable. Have Cortes fail. The Aztec Empire will still crumble, smallpox will still utterly destroy the place, but a powerful successor state can emerge which can probably hold on into the modern age. The place will be a free for all for a century, but European enclaves in Mexico are unlikely to expand to conquer the place. It'll be as close to a post-apocalyptic society as ever created on Earth--massive epidemics still ravaging the people, the world everyone knew shattered, new technology, new everything, apocalyptic cults, and above all, MASSIVE amounts of warfare, spurred on by European powers. But I'd have hope some society can keep independent in Mesoamerica, even if there eventually is a "scramble for Mesoamerica".
North America I have no hopes for. Barring alternate agriculture, any society that keeps independence will become a European protectorate. At best, remember. And this wouldn't be quite alternate agriculture, but introduced agriculture might work. Like try and get rice or buckwheat established in the Pacific Northwest by way of East Asian shipwrecks. The Northwest has conducive climate to both crops, and an Asian might recognise a plant known as wapato, of which a relative grew alongside rice in paddies. Probably an independent POD, but it could happen after Columbus and give the Pacific Northwest peoples a bit of a fighting chance, at least to become a protectorate of a European power instead of the decimation and conquest they endured OTL.
I was about to write a post about the Inca, and then read down and saw that you specifically said "north anerica". With a POD as early as 1492 I think you can pretty much take any Native Nation and want them enough to maintain independence. You've got 100 years before Europeans begin successfully settling north of Mexico, and then another 200 after that before real power projection beyond the Appalachians is possible.
You're mostly right, but
any native nation is a bit of a stretch. I don't think the Plains Indians, for instance, are capable of being independent without a lengthy period of colonisation to reshape their social structures, simply because their mode of organisation was totally alien to the European model which has become the internationally recognised way of organising a society. I'd further restrict it to those groups which had decent numbers even after European epidemics--so probably a group from the East Coast, Great Lakes, and the Pacific Northwest cultural areas. And the East Coast has the obvious issue that its ground zero for European colonists. And I didn't mention California Indians, but they seem too divided to ever be able to withstand Europeans--the fact that indigenous California has one of the greatest diversities of language in the Americas is telling. There's also the fact that any organised enough native Californian society might end up exploiting the gold resources there, which will attract attention of the very negative sort from Europeans.
Comanche are probably the best choice, or maybe even the Metis. Since the US can use them as a buffer between them and British Canada.
No, the Comanche definitely are not. Their social structure and mode of organisation is completely incompatible with something like the US or any other sovereign nation. They could never constitute a country on a Westphalian level without giving up everything that gave them such an advantage. And since the age of steppe peoples was over before the Comanche came to power, their days are numbered--it's only a matter of
when they would lose once the US (and arguably even the Republic of Texas) came onto the scene. They have a crippling demographic disadvantage--the bison were declining since the late 1700s in their range, and even their shift to cattle ranching didn't save them, since one bad winter or two will kill both cattle and deplete bison stock (further) causing starvation. Further, a key part of their economy was based on bison hunting for trade to Europeans. That's also going to deplete bison numbers as we saw. Incidentally, another key part of their economy was raiding other Plains Indians as well as Spanish/Mexican/American settlements, which certainly doesn't endear them to their neighbours. The latter can be controlled, but in return, the Comanche tended to demand gifts which at times basically amounted to protection money and proved to be very annoying for Spanish officials to have to pay.
The same applies to any other Plains Indian group. They are among the last cultural groups of American Indians I'd expect to ever constitute a sovereign, unconquered nation in a world that has any colonisation of the Americas at all.