Hey guys,
I'm a new user to the forum, but used the results section heavily a couple of years ago and am using it again this year.
@Blurry, I went to UIC for grad school until 2010, and I lived in Bridgeport for a time. Bridgeport is a good place to live if you're not really into night life. My friend and I lived in a very affordable 2 bedroom apartment for $750/month. Granted, it was really small and it didn't look nice, but there are other places that are affordable and a lot nicer looking. Because it's not really the south side it's not dangerous. There are a good number of families that live around that area. You can take the train to UIC campus (you'll have to transfer once), or there's a number 8 bus I used to take that would take me right to the East Campus, and it took maybe 15-20 minutes.
Alternatively, you can live closer to campus. Right south of campus is called University Village, but those are nicer and pricier apartments probably into the thousands per month. Some undergrad students and grad students live there. There's also another neighborhood called Pilsen, which is close to UIC campus that is really affordable. It's a primarily Latino neighborhood, and most of the streets are safe 'cause there are alot of families (my friend's apartment once did get robbed, but that was because he lived on the ground floor and the door was very conspicuous).
Right now I live in Chinatown, which is also a great place to live: Close to trains, good restaurants, and rent is fairly cheap. The only caveat is you need to know someone to rent here: I tried living here about four years ago but couldn't get an apartment until I moved in with someone who already lived here.
@InquilineKea, it would be highly impractical to live in the suburbs and commute by train: There's one set of train systems that connect the city to the suburbs, and there's another set that connects the city to itself. As far as I know, there isn't a direct train from the suburbs to the UChicago area.
If you are not going to live in Hyde Park (but you want to live in the city nonetheless), you can drive or take the train/bus. If you take the train I think you'll still have to transfer to a bus that'll take you to campus (you can take the red or green line). There are buses that go directly down there, too, but I'm not so familiar with them.
Hope that helps!