Midway ParkSavers is the best! They have an online coupon for a free day. They are located right outside the Orange Line train entrance, so you don't even need to take a shuttle. You just park, walk across the street, and enter the airport by the train station. I hate the Midway-owned lots because the shuttles are a zoo; if you're not assertive, you'll find yourself being elbowed out of the way and not even getting on before they fill. The only bad thing about ParkSavers is that some of the spots are small/tight if you have a large vehicle, so choose wisely.
Barb