Martin's Campground is in Joliet--did you eliminate that one from consideration for some reason?
It's not a resort or anything, and the noise from the interstate is noticeable, but as you found, it's pretty slim pickings in the Chicago area. Pretty much nothing in the way of amenities--we used it as a home base.
We stayed there a year ago for one week and went into Chicago on four of those days. We took the METRA train from the New Lenox station, which is a few miles from the campground. It's not a short trip into town, but since you'd like to be near the Speedway, too, it's quite well located for your purposes. And there's nothing closer to Chicago anyway, so you might as well be close to the Speedway.
Oh, wait, I just read the reviews. It's really not that bad. Here's a photo
You can see the front of our motorhome between the trees, and from there, the noise from the interstate wasn't enough to disrupt sleep.
Our motorhome did get to swaying due to the holes in the road, but the site was fine and despite looking like it's sitting on a hill, leveling wasn't an issue. Hookups worked fine.
I read in one of the reviews that the place is for sale, which is a shame because it's a decent option for the area. We chose it over Leisure Lake down the road, which is some sort of membership place open to Passport America or something. It's much more of a resort, if you're interested in that. But we had trouble getting someone to answer the gate phone and just didn't get a good vibe once we got in and drove around. Also, most of the sites available to us were water/electric only, although they do have a honey wagon service and there were a lot of long-term looking rigs in W/E only sites.