Even if you could find a lot in downtown Chicago with a space to take your RV it would probably run you about $75.00 a day. That would be just for a parking space, no water, no electric, no sewer, no anything. You would have to try to find a CG way outside the city but still close enough where you could catch the Metra to get into the city, or drive a toad in.
We spent some time in San Francisco this summer. We located a good CG across the bay. We drove our truck to a free ferry parking lot and had to take the ferry back and forth to the city each day.
Just keep in mind that a lot of CG's that are close to major cities and have public transportation are probably more expensive.