There is a new parking deck overlooking Midway - I've not been up there yet but I've heard it's great for spotting. The park on 63rd and Central is pretty good - I've never been hasseled there. There are a few businesses around the area that offer good views - White Castle, Giordano's, etc. Also over at the Southwest hangars on 55th there is a parking lot with a fence bordering the taxiways, if you're not there for too long the cops don't mind you taking a shot or two.
As for police - as long as you don't do anything stupid like put a ladder up against the fence, you should be OK
. When approached - just make it clear that you're an aviation photographer and you're there to take a few aircraft photos. It helps to have an example or two of your work with you. The Midway Special Police are friendly and usually somewhat accommodating. O'Hare cops (especially Bensonville) can be real . . . . difficult.
Good luck, have fun!