We just recently stayed at the wonderful Paul Wolff campground in Burnidge Forest Preserve in Elgin, IL. Water and electric at campsite, with a dump station. Literally two miles down the same street (Big Timber Rd) is the Big Timber train station, with a large parking lot. Check out the Chicago train routes online. Big Timber station is the last stop on this particular route, and I think the train doesn't stop there on Sundays, so check out the schedule.
We drove our car into Chicago. Would never want to drive the motorhome in the city.