Suggestion...

Schaumburg, 06C, fly into Schaumburg Airport and either a rental car
with AVIS in Schaumburg (847) 330 2847 (tell them Patrick from Hawai'i
sent you) or you can jump on the Metra train which has a stop at the
Stadium adjacent to the airport, it can take you downtown for about 5
bucks one way, within the hour

Fly into Lewis University Airport (I don't remember the Identifier),
rent a car at the AVIS station thats inside the GA terminal.

The upsides are free parking (last time I was at either a year ago),
and one of the most top-notch FBOs in the US, from my experience. Also,
it's a lot nicer to fly out of a basic small airport than it is to deal
with an arrival at Midway, especially on your first trip when you're
unfarmiliar with the airspace.