I am speaking as a Chicago native and not as a UIC, UChicago or Northwestern student. As for UChicago, make sure you know where you are looking. To the west of campus is the Washington Park neighborhood, which is one of the most dangerous neighborhoods in the Chicagoland area.
If anyone is looking for places to share, Wrigleyville can have some decent deals (with rooms at about $700/month). If you are open to renting a room instead of having your own apartment, that is always an option. Also, Wrigleyville makes it easy to get to all three campuses via the CTA. Then you have Lincoln Park, near DePaul, which is just a tad bit pricier than Wrigleyville. If you want to be in a place with a lot of shopping, parks, cafes and whatnot, go to Lincoln Park. If you want to have bars and Cubs games, go to Wrigleyville. Both are places that are great for young people, but I would say that Wrigleyville is more for the party types.
But you don't have to go into the city either. If you can get a place close to a Metra station, the suburbs can save you quite a bit of money. I lived most of my life in the suburbs in the northwest (Schaumburg, Hoffman Estates, Algonquin). These are nice places to live, but don't have great access to Metra stations. In DuPage County, you will have better luck with Metra station locations. It can take about an hour via the Metra to get into town, but you don't have to deal with traffic. The Metra is a better choice for those going to UIC, but not as much for the other campuses.