I would check with campgrounds in the northern areas such as MI, WI, other states as most campgrounds close after Columbus Day in OCT.
Now If you are planning on camping near Chicago IL., I would look at campgrounds about 1/2 to an one hour drive away. You might want to look into public transportation and take that into the city. There is a lot to see and do in the Chicago area; such as the Museums, Shed Aquarium and the Willis Tower and the John Hancock center. Plus the ladies always like to shop on the MAG Mile.
2016 34RL CC; 2008 Ram Mega Cab 2500HD, 6.7L, 68RFE 6 speed, 4X4, Smarty S67