Friends Creek is about 15 miles east of Decatur and about 3 miles off I-72.
Just east of Springfield is a city park at Riverton, IL on the Sangamon River. It's only about 1/4 from I-72 but is about 2 road miles to get to it on US 36. It's not well marked to find. If interested in that one I can get you the GPS coords.
Around Springfield, 7 miles south of I-72 on I-55 is the Double J. Easy to find, easy access, quick on an off the interstate. Fairly decent campground.
Those are your choices as far as close campgrounds. Personally, I'd do Double J.
Camped in every state