Cumberland El stop (CTA) charges 1.75 a day, I think it may be more if your over night. Also, get a map of the el stations, and a map of chicago and find parking on the streets 4-5 blocks from the station. All around the stations it is permit parking only until you get 3-5 blocks away. All safe nieghborhoods to leave your vehicle, I know because I live there and grew up there. Look into Harlem station and jefferson park (both are just a few stops from the airport). It may take a bit of finagling at first, but hen youll find a spot and no one really bothers you unless your there for weeks at a time
Good luck