Question is what do you want to do in Chicago? If you plan to spend some time touring the city, three suggestions:
DuSable on the near north side near Navy Pier and Michigan Ave. Burnham on the near south side near the museum campus. Burnham puts transients on the T docks at the end of each dock. Both DuSable and Burnham are within long walks to everything in the downtown area. Both have access to excellent bus networks.
For the closest to the loop (downtown), and the greatest views the mooring balls at Monroe Harbor are great. You must use (security) the harbor provided launches to get back and forth from the boat. Good system and part of the nominal nightly charge. If you take a mooring ball stay away from the center opening of the breakwall if you can. As of yesterday there were plenty of open mooring balls.
If you plan on spending time in Hyde Park (University of Chicago) then the 31st street marina could be considered.