I wanted to thank everybody for the advice (and bump the thread for future Chicago residents).
Thought not there yet, I have secured a 2 bedroom apartment in Edgewater that I am very happy with. A little pricey (compared to PHX), but I got all I wanted (A/C, washer & dryer, parking), for around $1800 a month.
I was really on the fence between Edgewater and Evanston. Knock it if you must, but living in a college town, IMHO, can't be beat, but since car ownership (and commuting) seems to be an inevitably, I might as well live where I would want and just drive.
Really looking forward to getting out of the heat (and yes, I'm aware of humidity, I'll take it over the 113 today).