Congratulations, citychild!
I am a student at the University of Illinois at Urbana-Champaign and will be conducting my internship in Chicago starting in August. [We conduct our internships AFTER we've completed our coursework.]
From what I've heard, Roger's Park is a very affordable area for students.
If you're okay with a commute, I'd look into apartments around UIUC as well.
The best way to find a place, IMO, is to go to the city, drive around, and look for places. When I went to Chicago with a friend to find her an apartment, we saw lots of ads on the sides of buildings. Maybe they were advertised online as well, maybe they weren't. If you don't have the time, money, or desire to just explore, I recommend Craigslist and finding a website that allows you to search apartments all over Chiago.
I've been browsing Craigslist also for apartments (a friend of mine found her apartment through Craigslist and it's a VERY cute place) and that isn't too bad.
Best of luck!