I grew up on the North side of Chicago and also didn't feel like UChicago had a very large presence. Now that I work in the research world (both in CS and biomedicine), it's very obviously the dominant institution in Chicago. Northwestern comes in at a distant second and UIC isn't really in the race. I'm not sure about their undergrad education but if a student wants to have access to teachers who are also leading voices in their fields, UChicago would be a better bet than other local options. Nationally you would have to look to places like Harvard or Stanford to do better.