I used to hunt the kaskaskia river public land in St. Clair prior to owning private ground. The IDNR has a crude map (link below). Might be worth taking a Saturday and driving the roads and see where there are parking lots. I’d almost bet there is access points wherever there are roads. For the best hunting, put in a boat and drive to spots where there are no roads. I used to take a POS jon boat and 6hp johnson and drive my spots in the boat. The further away from people the better your hunt. There are many slews and creeks so it may be impossible to walk away from the crowds. Also, spend some time on Google Earth and follow the river and you should be able to see where roads provide access to the public ground. Google Earth is a wonderful scouting tool but nothing beats putting boots to the ground. I used to kill lots of deer in those river bottoms.
http://www.dnr.illinois.gov/hunting/FactSheets/Documents/KaskaskiaRiverHunterMap.pdf
If you are serious about hunting public land, you should check out onXmaps that can run on a Garmin GPS or even a smartphone. Great thing about these maps is that is shows where the public and private lands are. Unless things have changed, the IDNR does not have the property boundaries marked very well.
http://www.huntinggpsmaps.com/