A lot of people stay in the apartments behind the hospital (Prairie Shores)...you can do a short term lease there anywhere from 1-6 months but the only thing is that they are unfurnished.
You may want to double check on the status of the hospital. I heard from many of my friends that it is closing in June and this past year, Michael Reese dropped out of the Match 2 days prior to ROL's were due.
Here is an article on its closing.
Eight Forty-Eight - Michael Reese to Close?
I don't know how this is going to affect students doing their rotations in May and June.