Divisions

 You have the original six figure division: The Northeast, the Feudal Core, the Gulf, the Plains, the Desert and Cascadia. (Quebec, Alaska, and Hawaii being outside the purview of the continental U.S.)

Cutting it into three, you would have the Forest Zone, the Grassland Zone, and the Desert Zone. Of course, the Gulf and the Pacific Northwest could be argued to exist outside the climactic designations, but as relatively narrow slivers of land, they could be said to still be part of their respective spheres of influence. The Gulf Coast would be a transition between Mainland America and the Caribbean, and "transition" means containing mutual elements of both cultures. Cascadia would see a lot of back and forth between the desert nations, and the District of Columbia is very much a Pacific Northwest society situated in the drier parts of the former Oregon territory.

You could say there's the division between the East and West, the delineation being the Mississippi river. You have the Non-Denominational sphere, and everything else. Eastern America is much more agricultural and populated. Western America , even when Christian, has become more esoteric, and is significantly less populated. Half of its population is composed nomadic herdsmen, and so even the settled communities (Which would probably very often be only a couple generations from nomadic hordes) would have values reminiscent of tribal societies. Once again, the Cascades would be an outlier on that front, but because of its distance it would still possibly have more in common with its nomadic neighbors than agricultural counterparts in the East.

East and West has recently seen the stark differences, in an East experiencing record precipitations, and the West experiencing droughts and unprecedented heat--even in the normally temperate Pacific Northwest.

Spidey

 Whenever people talk about Medieval America or post-apocalyptic fare one of the first things we jump to is talking about pop culture of today becoming "legends of old", and in some cases, the basis for religion. The latter is something I try to avoid, and even the former I believe in tempering it a little bit. It stands to reason that over a thousand years, a lot of movies and television are lost to time. I've mentioned comic book heroes potentially having a leg up, because of the relatively low tech but highly visual nature of their storytelling. But even among then, I sort of imagine Spider-Man having a particular status. I've mentioned him in toys, theater, even heraldry. I just have this inkling of him being enduring, where if any other heroes are remembered, he will be. It's a hill I will die on. Why?

Well, first I just think he has a look that is both relatively simple but distinctive. As I've mentioned, puppeteers don't have to work too hard on carving a face, just drawing a very simple body and painting it with webs. He's always been a very easy character to make plush toys and ornaments and the like without losing something in the translation. I think he also deftly embodies classic and chivalric heroes seen in the west, but also the animist and abstract beings from Eastern or indigenous folklore. A true melding that we would see be common in Medieval America.

Something that struck me as interesting was that in the first half the 2000's (when White first created his page!) there was a large trend towards movies with historical or mythological themes, which I would say officially petered out around 2007. Lord of the Rings, Gladiator, 300, Pirates of the Caribbean, and even some lower level performers like say, Troy. And yet, during this time, the most popular franchise was the Spider-Man one. This really seems to indicate that even in a culture where stories are about swords and arrows and armor, (because that would be people's sole frame of reference) Spider-Man would still have a place in it.

I've also mentioned before how Thor would benefit from a strange "foot in both worlds" energy. He is a character from the actual middle ages, who features heavily in books about mythology. (He even gets name-dropped in the Michael Berenstein trolls book.) People have been talking Thor for a thousand years and it stands to reason they would talk about him for a thousand. But because he has seen relative popularity as a Marvel comic, this also means you can't talk about him these days without talking about Marvel comics. So the Marvel Universe would sort of get brought along for the ride (a case for his fellow Avengers as well) and as Spider-Man is Marvel's most prominent character...

An interesting stat is that  in 2018, Spider-Man had appeared in separate movies--both Infinity War and the Into the Spider-Verse. Both were produced by different studios, which, granted, one was a cartoon and it was largely done with an accord between both parties, effectively still meant that Spidey had a rarefied status usually only found with public domain characters like Dracula and Snow White, or real life historical figures like Wyatt Earp. 

Also, his main bad guy is goblin. A medieval style goblin.