Well, Devil's Lake will be hard to beat - a beautiful place.
But there are several Illinois state parks within 3 hours of Chicago.
Starved Rock, as has been mentioned is a great one.
Look here for others
And these are a bit farther west, but many still within your driving time
Of course, if you get stuck on the Dan Ryan Expwy, I don't think even Grant Park is within 3 hours driving time!