Because I love hanging out on college campuses I have to reply.
UChicago: Ditto on what has already been said. It used to be said that it was a place where the students had to "marry the library for 4 years to get a degree." Maybe that's where they all were. It is for hyperintellectuals. Nice place to visit, but I don't know about going there.
DePaul: Nice campus atmosphere! A few years back it was known to rank #1 in some "student satisfaction" survey. I've never heard anything bad about it, and Greek life is really growing there.
Loyola: I worked here for a few years; and my 3rd brother went here. The Jesuits are educators. I like the idea of a Jesuit education, but personally prefer Marquette (Milwaukee).
Both of the DePaul and Loyola are excellent back-up/safety schools for an intellectual student.
Northwestern: I saved the best for last. My 2nd brother went here. It has a wonderful atmosphere academically and socially. Evanston is a neat town. Sigma Chi, SAE, and APhi all have their national headquarters here. I would feel very safe sending a student here.
One thing I love about Chicago is all the different colleges and universities. We have such a variety. I remember when my 1st brother was going to college and the whole family took a trip to several of the Eastern colleges. We both ended up going somewhere that we had never seen before and took a chance. Going on those pre-college trips is alot of fun but its alot of work, too. Good luck to your daughter.