Hmmm. If I had it to do all over again I might live in Bucktown. Pretty cheap, pretty urban, and pretty easy to get where you need to go. As it was I lived in a couple of places in Lakeview and that was great. A little tough to get to the airport, though.

That said, there are plenty of good neighborhoods in the second post. And I think your $850 is going to be the limiting factor.

Edit to add: there are a TON of young, attractive girls (or boys, depending upon your preference) in Chicago. You'll have a great time.