I'd vote New Orleans out of your three options. But if I could choose any one city in kind of that same vicinity without a doubt it would be Memphis. Followed closely by Nashville. Great fun at night with all the bars and music and during the day there is plenty to see and do to keep you occupied.
I also like the idea of going to less tourist-y places but I think that's better saved for a second or third trip (how many are you on now dbb618?)
Gentlemen, we just seized an airfield.
That was pretty fucking ninja.