TonyC's suggestion is a good one: I sometimes park on State north of 18th St. and take the 29 State St bus north to the loop. There are no meters, and having my car across the street from the police station feels pretty safe! But of course I just do that during the day, not for a whole weekend as cbdurr seems to want to do.
Let me mention another possibility. cbdurr, even though your hotel may be charging $30/day for parking, it should be possible to find an independent garage near your hotel for a much lower rate.
Here's a link to a listing of parking garages:
http://www.bechicagoil.com/parking.html
You could try calling one near your hotel and see if their rates are within your budget.