I completed my bareboat certification years ago (2001-ish) with a company called Sailboats Incorporated.
The do instruction and bareboat chartering.
They have a long standing presence right in the heart of downtown Chicago--Monroe / Du Sable Harbors to be exact. It's an excellent location. They have a few other bases too (Lake Pippin, MN and Bayfield, WI near the Apostle Islands of Lake Superior).
After the course, I chartered with them quite a few times--sailed their boats around Chicago, and as far away as New Buffalo, MI. They were always great to work with. Their fleet is older, but maintained acceptably.
Wednesday and Saturday evenings at Navy Pier there are short fireworks displays. It's not much of a display--but to take it in from a boat is awesome.
Another company of interest is Michigan City Sailboat Charters (although it would be a crunch to sail to Chicago, take it in, and return in two days).