There is also a music festival on.
Would you advise anywhere to travel onto from there?
Are you going to Lollapolooza in Grant Park? If so you may want to stay more in the downtown area, as it would be closer.
My girlfriend is currently finishing her doctorate in psychology in Chicago, so I've been to the city loads of times. For most people visiting Chicago, their list of must-see places includes the Chicago Instiute of Art, Wrigley Field (one of America's most famous baseball stadiums) and Navy Pier.
The northern parts of the city are nice and quaint filled with typical Chicagoan architecture. The southside is pretty sketchy, as are parts of the westside. Transportation is cheap and relatively quick, although some tourist spots such as the Field Museum and the Museum of Science and Industry (once used as part of the World's Columbian Exposition as referenced in the book Devil in the White City) have to be primarily accessed via bus only.
A great place to eat on the northside in the Wrigleyville area that is cheap is Tango Sur. It's a small Argentine steakhouse and is often voted one of the best cheap eats in the city. I believe it's BYOB. You'd have to go early (i.e. 5pm at the latest) as it gets packed very, very quickly. The service is a bit slow, but the food and the portions are amazing.
Additionally, there is a small movie theatre a few doors down from Tango Sur called the Music Box Theatre, which runs foreign, classic and independent films. The theatre was originally built in 1929 and consists of a large, restored original theatre and a small adjacent one added in the early 90s. It is a great place to watch a film, as it's like going back into time, complete with an organist playing before the film begins. They also sporadically have film premieres there or presentations by famous filmmakers and critics such as David Lynch, Roger Ebert, Spike Jonze and so forth.