Still plenty of land to develop and
It does make you wonder what the USA looks like, and does, without the Civil War.
Well, without the Civil War (presuming slavery is limited in the Constitution, the south buys that, the old Southwest goes the way of the old Northwest, and Eli Whitney trips over a rake or something) you might be able to make the case for slavery not becoming the economic and political force it was historically, but still have the continentaL US develop essentially as it did historically.
Even by the 1860s, that leaves plenty of land in what became the Lower 48 to develop and populate, and the last gasps of Indian sovereignty (northern and southern Great Plains, Great Basin, and Southwestern) cultures to force into the reservation system.
At that point, industrialization is going full blast in New England, the MidAtlantic, and Great Lakes/Old Northwest, so that should absorb plenty of energy as well.
Alaska may get picked up more or less as historical (the driver was from the Russian side, largely) and the economic penetration of Hawaii was in place from the whalers/missionaries three decades earlier.
Dollar diplomacy in the Caribbean, Mexico, Central America, and South America (to a degree); presumably trans-Pacific trade - the Open Door may or may not become policy.
Basically, I could see a level of engagement in the world, generally, about a decade ahead of the historical curve, absent the Civil War.
So more US diplomatic involvement in Europe and Asia, but the willingness to be involved in much more than the "punitive mission" of military engagement seems unlikely - the US was pretty content to focus on the Western Hemisphere in this era, absent the outliers like Samoa etc.
The US may take a more active role in Monroe Doctrine enforcement (I could see a US absent the Civil War being much more actively opposed to the French and Spanish interventions of the 1860s, to the extent they may not happen), which presmably leads to more of a partnership with the Latin American republics, rather than a dominant party type role.
Rough guess, absent the Civil War, "this" US in 1875 may look more like the historical US in 1885, and so on - without the civil war, however, the dominance of US politics in the Nineteenth Century by the Republicans is less likely, so there might actually be more political pluralism. A Republican-Progressive alliance in opposition to a Democrat-Populist one, and vice versa. Racial and gender politics will be interesting, certainly.
Prohibition may come in earlier, although without a lasting Republican-Progressive alliance, it may not come in at all.
Lots of ripples, obviously.
Best,