Maybe some info in these sites will help you decide. In several cases, phone numbers are listed so you can contact the campground directly to ask about the services and if the sites can accommodate your Airstream.
In Southern Illinois, you'll find a whole range of camping options -- from forest to near city sites that are all in close proximity to natural wonders like the Shawnee National Forest, Trail of Tears State Forest, Ferne Clyffe, as well as tourism activities from wine trails to antique shops and arts festivals to bike and walking trails and fishing and hunting spots, and wildlife habitats.
Southernmost Illinois Tourism Bureau | Visit Southern Illinois
Visitor Activities - Crab Orchard - U.S. Fish and Wildlife Service
If you haven't already used it, RV Park Reviews
is a helpful resource. Search for campgrounds near the following locations: Goreville, Carterville, Marion, Alto Pass, Cobden, Makanda, Vienna, Metropolis, Harrisburg, Elizabethtown (IL) . . .
It's a wonderful area. You have lots of options. A word of caution, recently there have been several hikers who have gotten lost in the Shawnee National Forest and other forest areas and had to be rescued by search parties. Recently someone did fall to their death in the Garden of the Gods.