SJFlyer, I'd have to agree on MDW. For training you can't beat PWK, DPA, or 06C (Palwaukee, DuPage, or Shaumburg-each one is at least 45min drive from downtown with no accessible train) For a great experience, Midway will be pretty fun. If you're lucky you might get to land in front of a SWA or ATA 737 full of folks wating FOR YOU to land in our bugsmasher. That fee ain't bad, Meigs used to be something like $50.
One of the FBO's should give you a ride to the Orange Line, or depending on where you stay (if you are staying overnight) you might be able to get an airport shuttle to a hotel downtown.
Feel free to PM me if you are looking for restaurant recc's-- give me a price range and an ethnicity and I'll give you a list of good places.
Have fun!