There's a hotel about two blocks away from the studio that'll charge you $60-$65/night. I'll PM you with more details on that one.
No, a rental car is certainly not needed. You can get a shuttle to take you back and forth from the airport, and it's only something like $31 both ways.
As you may or may not know, I'm from Stillman Valley, IL, which is all of 10 miles below Rockford, so I can tell you that flying isn't bad at all. You can avoid most of the problems with flying by flying Southwest, which flies out of Midway instead of O'Hare. Having flown out of Midway the last two times, I can tell you for sure it's MUCH better than O'Hare, not to mention cheaper. Also, since you're so close to Rockford, you can just drive to Rockford and take a bus. It will take you directly to/from Midway for, last I checked, $20 each way. It's really not a hassle.
EDIT: Van Galder also runs out of South Beloit, according to their website. Even better!