The best parking value in the Loop is usually the Grant/Millennium Park underground garage, with entrances on Michigan Avenue and Columbus Drive just a few blocks southeast of the Renaissance. I think I remember daily rates of around $20, but call 312-616-1544 to check.

You'd need to go a good mile west of the Renaissance to get cheaper rates at surface lots.

The Cumberland garage is among the best parking values within city limits, even if it's an hour away by train. (45 minutes according to the schedule, but service has degraded considerably.)