I think Herrick Lake might have some camping. I'm not sure how it could be enjoyable, though. Anything remotely close to "open space" in DuPage County tends to be absolutely packed.
I did two camping-by-bike trips last year and had fun on both. Both started on the Fox River Trail in Genevea/Batavia/St. Charles. One went out the Great Western Trail to Sycamore, then on to Oregon (where there are plenty of camping opportunities). The other went down the trail until it ended, the continued on roads to the I&M canal. From there I headed west to the Hennepin, then north on the Hennepin feeder and up into Dixon. No shortage of places to camp on either of those.
Not sure where in the Chicagoland you're located, but a metra ride to one of the farther outlying suburb could make something like Marengo Ridge or Shabbona lake a fairly relaxing day.
The pic is the second night of the I&M/Hennepin canal pic. I was I was with another dude, and we ended up riding well into the dark. These little camping areas are all over on that trail. Pretty cool... and no tent needed if you've got a tarp!
https://picasaweb.google.com/lh/phot...eat=directlink