Columbia has a reputation for being quite liberal even by ivy standards. I don’t think overall it is as liberal as Brown or Yale but it probably comes righter after those two.
Columbia pops into my head first as well. Similar core, in big city, similar size, rigorous…but similarly selective and if OP is looking for matches/safeties similar to UChicago, Columbia wouldn’t be that.
Columbia’s School of General Studies is much less selective than Columbia College.
GS apparently is oriented to military veterans and other “non-traditional” students who have been out of HS for at least a year (which may not be what the OP would want). However, as I understand it, General Studies students have access to most of the same courses available to Columbia College (or Barnard) students. I’m not sure if that includes the Core courses. I’m not necessarily recommending it as the next best, less selective version of UChicago … but it’s an option the OP might want to consider.
GS is a huge “Continuing Education” college. I don’t think the OP would find the academic community (s)he seeks, even though GS is part of Columbia. Among other things, it is a non-residential college, so that students have to provide their own housing in NYC.
Columbia GS is not even an option for traditional students – that is, if the OP is now in high school in the process of choosing which colleges to apply to, then that student is not going to be considered for admission by GS. The whole point of the school is to serve the nontraditional students – it’s not some mythical back-door entry into Columbia.
And although the acceptance rate is higher, the GS students on average reportedly have higher GPAs than the Columbia College students. It’s not a back door; it’s an additional door: one of the four undergraduate colleges of Columbia, with Barnard, Columbia college, Columbia SEAS. All of the students of all four colleges can take the same classes and can be part of the same social organizations, and use the facilities. It’s the same education.
GS also doesn’t have great FA. If a student interrupts his/her studies for a short while, they are eligible for GS.
I think the OP would need to clarify whether s/he’s trying to replicate aspects of the UofC academic program, the social atmosphere, some other je ne sais quoi, or all the above. To me, the Core curriculum, small discussion classes, urban setting, and presence of graduate programs all contribute to the UChicago “vibe”.
As for Columbia’s School of General Studies, it seems to offer nontraditional students pretty much the same education (and degree) other Columbia undergrads get (esp. if you think the essence of Columbia is in the curriculum, more than the social experience of being in a cohort of traditional Columbia College students.) Not that most HS students would be willing to take at least a gap year just to qualify (and also forgo the on-campus dorm experience, bonding, etc., associated with a more traditional path.)
A good litmus test: when a library becomes at least one of the significant social hubs on campus.
This applies to Cornell, Yale, Columbia (a bit), MIT (but more STEM oriented), Swarthmore, Johns Hopkins, and, a little down the food chain - Case Western, University of Rochester, Reed, Carnegie Mellon…