I looked at UAB...great place...loved interviewing there. Great people. Great facilities. Lots of money supporting the program. They even have their own librarian just for the anesthesia department to assist you in finding the best articles. The chair who has been a major player in the department was in the process of leaving--said he wouldn't be there this year or the next (I can't remember). He said it wasn't for anything bad...just time to move on. You'll just have to look for yourself. In short...I'm sure you'd get great training at UAB.
One place that is missing from your list of southeastern programs...Wake Forest. As with UAB, I loved interviewing at Wake. Great facilities. Great residents. Great Faculty. Multiple Oral Board examiners. Cutting Edge. Well funded. Just a first class program all the way. Their department certainly is a leader in Anesthesia. Again, it just depends on what you are looking for in a program.
Just keep an open mind. Enjoy your interviews and really see how you fit in with the "feel" of the program. When you're looking at the programs that you've mentioned...you probably won't go wrong, which is why it's so important to find out (in 1-2 days as best you can) how the residents and faculty interact. Ask questions about how residents get along. Do you see yourself fitting in with a particular program.
I heard some rumblings last interview season regarding Vandy, but I don't know what the reality was...some people said one thing and others said exactly the opposite...probably nothing. I have a friend who is headed there and has had nothing but good vibes about the program.
Good luck.