Since you're coming from the south and heading to Michigan, look into reserving a site at Indiana Dunes State Park (not the National Lakeshore) in Chesterton, IN. Very nice CG with electric hookups, showers, dump station, etc. It is quite popular, so you don't want to just chance it for a site, especially on weekends.
There is a commuter rail station within a mile or two of the campground, which you could take into the city. Chicago is quite walkable, plus there are buses, water taxis, and I believe in summertime even a free trolley (which is usually too full to get on, but anyway) to get around with. (And taxis too, should it come to that.) No worries about parking if you visit that way, and you can see some of the major things in a few days. I suggest the museum complex (Field Museum of Natural History, Shedd Aquarium, Adler Planetarium), the Art Institute, Navy Pier and its huge ferris wheel, and just walking around Grant Park and enjoying the lakeshore & city skyline. Oh yes, there's the Bean too (just ask about it). You can't possibly see all of those in one day, but whatever suits your interests among them.