I'd suggest leaving Chicago mid-August and hitting the northern parks first. Then work you way down to Arizona and Grand Canyon and back to Chicago. Arizona and the southern national parks of Utah will be best in Sept/Oct.
Each national park has an excellent web site which gives you campground information, including closings, road information, things to do, etc. Check them all out before your trip. I, too, would not trying to do Yosemite on this trip.
Here is Yellowstone's site:
http://www.nps.gov/yell/planyourvisit/hours.htm