Chicago's CTA public transit system is fairly wheelchair accessible. When I was there I purchases a 7-day unlimited ride pass at O'Hare airport. The current price is $28 USD. You can get shorter and longer passes if you're not staying exactly a week. The pass start from the day you first use them which is really nice. More information about the pass can be found here
At this time every bus in Chicago is equipped with a ramp and should be full accessible for anyone.
The majority of CTA's train stations have elevators or ramps to provide access for customers with disabilities. There is a list of the accessible L-Train stations here.
Chicago disability transit offers door to door accessible service to anyone who needs it. The fare seems to based on where you travel so it's best to get in touch with them directly for more details.
There is a taxi service called Open taxi's that has a centralized dispatch. They offer immediate pickup or prearranged trips. Call 1-855-928-1010 or email them at
Although I haven't tried them yet I found a place that will rent you a handcycle. This seems pretty awesome if you're with someone who is able bodied since you can both go for a ride.