Flying to Chicago Midway
I've flown into Midway many, many times to visit my son when
he was a college student in Chicago.
As others have noted, be prepared for a fast approach. Also be prepared to shift over to a parallel runway once you're handed over to the tower (even on an instrument approach, once you've got the runway in sight). One of those runways is about 2,500 feet: I call it the kiddie runway, and that usually gets a laugh from the tower.
Don't be surprised if you get an instrument approach, followed by a circle to land on a different runway: even when the winds don't favor that runway. That's due to the traffic patterns into O'Hare.
In a low IFR situation, none of Midway's runways has a good approach lighting system. This is because its crammed into a residential neighborhood. So you might not be comfortable coming in at or near minimums without a half mile of lights to guide you in. On the other hand, you might find it very exciting...
Atlantic is the best FBO; Million Air is a distant second; and stay away from Signature. The problem with Million Air is that they can't accommodate an extension cord for heater plug-ins, because at night their ramp has to stay clear for the freight dogs who carry checks for the Federal Reserve. Atlantic will accommodate that kind of request, but you need to insist on watching it get set up properly. Signature charges an arm and a leg for hangar space, and two arms and two legs for deicing.
Its a quick trip by rental car into downtown, and all of the FBOs can give you a really cheap pilot rate if you ask.