There was a thread on this a few months ago. If you can ride the train (red line), you can go up to Quad's Gym (not the one Ed Coan trains at) off the Addison stop. It's not downtown, but it's not too far and it's easy to get to.
Eleiko has some sort of thing downtown, some guys at 70s Big Chicago went to some lesson or something there.
There are a couple CrossFit(TM) franchises down there, not sure about drop-in rates and just letting you use the equipment.