In the City you don't need a rental car to get around.
From Chicago's O'Hare Airport a cab to downtown runs about $50 with tip, or take an airport shuttle (blue vans) to your hotel for around $20. For the local flavor, board Chicago's famous L (light-rail) for $2. Midway Airport offers the same mix of service, and travel time to downtown from either airport is thirty-sixty minutes.
In the City you can rent a bike or Segway, hail a horse-drawn carriage, catch a party-trolley, water-taxi or double-decker bus, and explore the city through it's excellent mass transit system.
The L will take you into the city's neighborhoods, which are all pedestrian friendly. If it’s cold, or you’re running to catch a show, the city has about twenty thousand taxis that will take you where you want to go.