I was stationed in Gulfport, Mississippi for a few years about an away from New Orleans. Spent so many weekends there partying. Epic place for sure.
Def hit up a Cajun Swamp tour. I think it is near Slidell, La. Other than that, small towns will be the nothingness ya imagined the south to be. Plenty of nice scenario though. Not very helpful with specifics because I spent a huge chunk in the deeeep south, not in your path.
As far as in New Orleans, be careful just a block away from bourbon..and hit up the bourbon cowboy and fat cats. Stay away from strip clubs