Wirelessly posted (BlackBerry8100/4.2.0 Profile/MIDP-2.0 Configuration/CLDC-1.1 VendorID/100)

Technically, the McCormick Place Hyatt is closest, but it's hard to get to Comiskey (whoops, The Cell) from there.

Bike rentals can be had at the 'McDonald's Cycle Center' at the NE corner of Millennium Park, which is also downtown:
http://www.chicagobikestation.com/

Net recommendation: stay downtown, south of the river, and stop by in Chinatown (one stop north of Sox-35th) for food.