Lots of good suggestions here.
Note that St. Johns has a Santa Fe and Annapolis campus. The Santa Fe campus in particular is beautiful and is in NO WAY urban - it is on the edge of a wild/natural area. And no school in America is as devoted to a strong core curriculum as St. Johns, not even Chicago or Columbia. but it is TINY and a very niche vibe.
Another suggestion that wasn’t on the list so far is Lawrence University in Appleton. Check out its entry in “Colleges that Change Lives.” Not as well known as many other schools on this list, but excellent school, strong required core curriculum (and campus-wide freshman seminars studying everything from Miles Davis’ music to Greek Philosophy).
Just going off of other kids I have known who felt the allure of the rep of Chicago (as a place for kids truly interested in learning as much of the world’s “great ideas” as possible, in becoming broadly and deeply educated), one proxy way of thinking about the campus culture is looking at their graduates career choices (most have percentages on their webpages).
See how many kids are going on to grad school, or into non-profits, or education or other service, etc., vs. how many are going into finance, consulting, tech, pre-professional type things. Some schools (like Wash U in St. Louis) are heavily pre-professional. That often leads to a different vibe on campus, different approaches to learning in classrooms, etc. (for instance: many students interested in med school are terrified of getting a B, with good reason. This can lead to a lack of intellectual risk-taking).
You’ll find that many elite universities have a very high percentage of their recent graduates who go into finance/the professions/etc., while a group of small schools (Oberlin, Reed, Swarthmore, etc.) traditionally send a lot of kids to graduate school, and not so many into finance/professions (though more and more Swarthmore Swats are headed that way recently, it seems).