Hi I asked a friend and here's his response
I have several suggestions for campgrounds, but as for parking downtown Chicago, I don't- never drove into that part of the city in 32 years. There are some limitations on trucks in the city, particularly along Lake Shore Drive, that he should be aware of. I'd recommend for his parking questions, he post in the "campgrounds & parks" (similar name) section of the forum. There are others on here who are from the Chicago area who may be able to give him some ideas regarding parking.
As for campgrounds, his best bets will be a good 30-40 miles outside the city. (There are none in the city of Chicago to my knowledge.) If he is traveling there in the winter, he will have trouble finding much of anything closer than Utica, IL; very few northern IL campgrounds are open off-season. OK, assuming he's going during camping season, I'd recommend either Indiana Dunes State Park (near Michigan City, Indiana) or Illinois Beach State Park in Zion, IL. Both are near commuter rail lines into the city (which is by far the best way to travel into the city, IMO, and will make the parking question moot.) Both are popular, Indiana Dunes especially, and he will need advance reservations. Sites have electric hookups and the CGs have showers; no other hookups available, unless things have changed in the last 3 years. If he wants FHUs, he'll have to go a bit farther - Chicago NW KOA in Union, IL or (I think it's called) Hickory Hollow - something like that - in Utica, IL would be best bets there. The state parks are much nicer, IMO. Hope this helps!