Oddly enough I was idly kicking that sort of thing around in my mind yesterday... I'm in Rock Island County. Time is the problem for me, but let's kick it around anyway.
For a simple friendly get-together, nearly any state park would be OK. For anything more primative, I think private land or a Boy Scout reservation offers better opportunities. IIRC, we have a couple of regulars south of me, but most of us are clustered in the northern parts of the state - AFAIK, I'm the farthest West in IL.
Understand, while I think this is a cool idea, I'm booked one way or another most weekends, so I may not be able to participate personally.
WRT Scout Camps: There are 3 Scout Camps in this part of the state that I know of - ours (Loud Thunder), Ingersol (entrance actually in my council, but camp is WD Boyce's - about 45 min West of Peoria), and Canyon Camp (West of Rockford). Ingersol is probably the largest and offers the most primative opportunites AFAIK. I haven't been to Caynon Camp but I think Willie Vannerson has visited there. My local camp is probably too far to be a convenient drive for most folks, but it is available and has common boundaries with a 2,000+ acre county forest preserve (same name) with a decently sized lake and Mississippi River frontage on one side (the fp, not our camp).
So - you started this - what do you have in mind?
Tom