Just in case you cannot find a hotel that will allow parking, too, I recommend Midway Parksavers parking. It is closer and cheaper than Midway's shuttle lots...they charge $8 per day (tax included), but you can get a coupon for a free day so that will bring it down. They are located right across the street from the airport's Orange Line train station entrance, so you can walk right in instead of waiting for a shuttle bus. We use them at least twice a month for weekend trips, and although some of their parking spaces are tight, overall we really like them.
Barb