There are some campgrounds in the west suburbs. Google Kane County Forest Preserve Campgrounds. There is also Illinois Beach State Park to the north near the state line. Some people have dry camped at the Marshalling Yard just south of McCormick Place. The area around there has gone downhill, so your safety might be a concern. FYI, over 100 people were shot in Chicago over the recent long holiday weekend. As others have suggested, Indiana Dunes is your best option.
Should you have a pickup, stay off any Chicago street designated a boulevard. This includes Lake Shore Drive.