I'm pretty sure it's a high school... It certainly doesn't look like a college.
Then again, it could be that there's a community college section tacked onto the high school. I mean, there are middle-high school hybrids so it's not that farfetched.
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It depends on the campus. Some of them have specific visiting days, but otherwise you can just waltz into them. Public universities count as public property, and if the doors to a "hall" are unlocked and you look like a student it's fine. You can't just go into a classroom, but a lot of classrooms have windows you can easily walk by and take a glance inside. Regardless, you can always just go to youtube for video'd lessons of professors and see how college classes look and work that way.
Plus, as for public universities, they have things like shops, banks, cafes, etc that are totally public. My uni had one of each of those and a salon literally right next to each other and anyone from outside could easily walk to them. Only using certain facilities is restricted, ie libraries and gyms, and of course dorms are private too.