I defintely recommend Craigslist. You might have to wait a bit closer to your move date but you can still some places a couple months out. As far as neighborhoods, I agree with TL in that the neighborhoods here are very distinct and it very much depends on your personality and living arrangement. I live in Lakeview, which is about 5 miles out from the loop. Its close to the lake, young but not nearly as yuppified as Lincoln Park (which is just south), extremely vibrant, and close to Wrigley (Wrigleyville is actually part of Lakeview). Lincoln Park is expensive and yuppie but a pretty decent area overall. Roscoe Village is another neighborhood you might want to take a look at. Bucktown and Wicker Part are pretty Bohemian areas (although the yuppies are invading WP) but I hope you don't plan on bringing a car up there (or anywhere in the city for that mattr).
Chicago is wonderful, even in winter, which is definitely brutal. To me, it's got a New York look with Midwestern hospitality and friendliness. I've visited twice, once in the dead of winter and once in June. I love the neighborhoods, taverns, restaurants and people.
Chicago is a great town. If I were to ever leave Texas, Chicago would be at or near the top of my list of places to move. If you manage to get there before early June, make sure you check out the Chicago Blues Festival at Grant Park. It's free and it's an absolute blast.
Ditto. I even enjoy most of the suburbs I've visted because a lot of them still have that small town feel to them. I'd love to live somewhere like Deerfield or Libertyville (home of Tom Morello).