The Metra goes right by the Schaumburg airport on Irving Park road. However, I would stay away from that flight school. They have a bunch of nice new Diamonds, even a Twin Star, but the management of the flight school leaves a lot to be desired. The instructors there are knowledgeable, but the operation is on a shoe string budget and the owner has his share of run-ins with the FAA.
At PWK, which you can't get to unless you take a bus (which I am not sure is available anyway) from the Metra line from downtown Glenview or Northbrook is not a great option. You can read about Palwaukee Flyers if you do a search here. The only other school is American Flyers. Good place to rent/receive instruction, but Flyers is expensive.
Either of the two schools at DPA would work fine for you. American Flyers is there as well. They have a diesel C172 if you are looking for something different. I guess you can probably get to DPA from the same Metra line that goes past Schaumburg, but you might want to double check.
MDW is probably your best bet. You would have to do some checking, but API and General Aviators were there last time I checked (might now be called Midway Aviators). General Aviators was always a good place to rent and they had a variety of aircraft. Anything rented out of MDW is going to be expensive, just be prepared.
If you can somehow get to Waukegan and you have a few extra dollars, there is a club there called the "Stick and Rudder Club". It is a real good place to rent and they too have a good fleet (Cessnas) of aircraft.
PM if you have any more questions and perhaps I can ask some folks that I know that still instruct.
