OP- NYU Stern is about as opposite as you can get from U Chicago if you are looking at the “highly rejective” group of colleges. Seriously. People who love Chicago generally love an entirely different set of schools.
Stern is pre-professional to the extreme, highly competitive (with each other, not just meaning the work is hard), very wired in to Wall Street but not “learning for learning’s sake”. Stern students aren’t spending time pondering the meaning of life, or getting excited about the philosophy course they are taking which has radically changed the way they view history, society, politics, etc.
Kids who love Chicago often love Rochester, Haverford, Swarthmore, Wesleyan, Rice, JHU. Kids who love Stern generally love Wharton, Villanova, BC, Babson, Northeastern.
I think the bread-baking Firefighter who takes care of elderly family members could get admitted anywhere (no guarantees of course) so If Chicago is truly a love- maybe reconsider Stern? Other than being in the middle of a city and having a couple of similar looking buildings they have very little overlap in terms of the intellectual focus and experience.