There is Illinois Beach State park in Zion IL. probably the closest thing to a campground for Chicago. I believe you can catch the Metra train down to Union station which is just about across the street from the Sears Tower (I refuse to call it Willis Tower)! the Marshalling Yard is behind Mc Cormick place. it has security and is pretty safe!
As a Illinoisan that's all I can say. I avoid Chicago like the plague. I live in the NW suburbs, but grew up in the city and adjoining suburbs. I even have my routes around the city when I leave south!
Have a good trip!