I am a born/raised/had my early professional career in Chicago, lived 4 years in Phoenix, and now live in Austin.
If I were in your shoes, I would rule out Phoenix and focus on Chicago and Austin. Phoenix is not diverse, its cost of living is becoming very high (not so Cal high, but higher than Austin for sure, not sure about Chicago), and overall it's a very conservative area. There are some tech opportunities in Phoenix, but I think the lifestyle tradeoffs for someone like you are probably not worth it.
Chicago is very diverse, has a really great nightlife scene, tons of young professionals - it is a very vibrant city with tons to do and lots of opportunity. Obviously, many of the suburbs can get conservative, but the downtown areas of Chicago are fairly diverse politically and I'd say lean liberal (hence why they've had a Democratic mayor for the last 20 years). As you mentioned, the biggest drawback truly is the miserable winters. It's what made me finally leave at age 28 - the day I was walking down Jackson to my office facing a 10 degree temperature, 40 mile an hour winds and a -20 wind chill. That pretty much did it for me.
Austin is not really a cosmopolitan city like Chicago, but I'd say as far as small cities go, it has a nice active downtown, a good tech sector, great weather, decent cost of living.
I'd say if you can live with the weather, pick Chicago, but if you can't, Austin is a fantastic secondary option.
If you have any questions, feel free to PM me. Best of luck with your search - you have tons of opportunity ahead of you!
