I live near Chain O Lakes State park in northeastern Ill. I would suggest that you check it out as the campground is nice and mass transportation to Chicago is close by in Fox Lake.
The campground has a dump station but no sewer hookups like in most State Parks. The train ride to Chicago will take a little over an hour on the Metra train, and it will leave you off in the middle of the city. Millennium Park, Navy Pier, the Mag Mile shopping and museums are all near by. I agree with jim5306 on visiting during the daylight hours especially if your not familiar with the city. Chicago is a beautiful place and a lot of fun but you have to watch your six at all times. Crystal Lake is another place nearby that you can catch the Metra train into the city.
https://metrarail.com/ will show train schedules.