The location is not given, however enough Easter eggs lead me to conclude it's Los Angeles:
* There's a scene where Noa, Raka, and Mae are riding away. In the background, you see on the horizon a shape just like the first image below. Without a doubt, that's the LAX Theme Building.
* From there, they wander into an observatory. The only candidate in the area is the Griffith Observatory (second photo below). Not quite the same, but close enough.
(2/x)
Finally ... and this is a fairly significant spoiler, so avert your eyes if you don't want to know ...
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Mae rides her horse for days to arrive at <a location>. This location is immediately recognizable, especially if you're into astronomy or planetary science or <redacted>.
<Location> is about 750 miles from L.A. Assuming she rides 25 miles/day, it would take her a month to get there. Not entirely implausible.
As for a quick film review ... (4/x)
... It was enjoyable but very slow-paced. I would have edited out at least 20 minutes of exposition and "day in the life" scenes that really didn't advance the story much.
Hooks are left dangling if they want to do a Noa trilogy, but they could certainly leap ahead again if they wanted and we wouldn't really miss much. The (humans vs. humans) vs. (apes vs. apes) story is getting old. If it were me, the next one would be a remake of the 1968 film with the Icarus arrival and I'd end it. (5/5)
* Much of the location is overgrown with vegetation and collapsed infrastructure, but in at least one scene we see (overgrown) a pedestal with the V-shape atop. That matches the elevated car pool lane about the 110 (Harbor) Freeway, the third photo below.
* Most of the third act occurs near a collapsed bridge. It might be the Vincent Thomas bridge in San Pedro ... If 200-300 years have passed, almost certainly L.A. had a major quake that could have collapsed these structures. (3/x)