There are Taxi Stands at the lower-level curb front (outside of Baggage Claim) at each terminal at O’Hare Airport. At Midway taxi stands are located on the lower level curb front of the terminals, and taxis are available on a first come, first serve basis.
A taxi from O’Hare to the University campus will cost approximately $50-60 and take 30-60 minutes depending on the time of day and traffic.
A taxi from Midway to downtown or the University campus will cost approximately $30 and take about 30 minutes.
A taxi from downtown to Hyde Park will cost approximately $20-30, but note that although it is easy to hail a taxi in the loop it is difficult to find a taxi in the street in Hyde Park! There are taxi stands on the hospital campus (58th and Maryland) and in front of the Museum of Science and Industry (5700 S Lake Shore Dr) during museum hours.
You can hire a taxi. The two main cab companies in Chicago are Checker Cab and Yellow Cab, and you can hire one just by calling T-A-X-I-C-A-B, or 312-829-4222. You should call at least 30 minutes before your desired pickup time. It is also a good idea to make sure you know the street address where you want to be picked up and have a call back number to give the dispatcher.