Where can I park for three nights in Chicago?

I am flying into O'Hare to spend three nights in Chicago with a friend. My friend is driving in from Monticello. She will be picking me up at the airport. We are staying at the Palmer House Hotel near the loop. We are not looking to pay 50+/night to park. We will not be using the car at all during the three days. Where is an economical place to park with transit access? We wouldn't mind parking anywhere between O'Hare and the hotel, hop on a train, see the car in 3 days. Any advice?