See to me, New Orleans is a distilled version of the South, or at least my experience of the south. Miami is an example of "not part of the south" But then again I grew up in Biloxi, about 2 hours from Nola taking your time, so we spent many weekends there. It's a horrible, dirty, dangerous, smelly city... And its absolutely wonderful. Of course that's mostly just certain parts... But those are the best parts to visit.
The strip between Nola and Mobile is quite different than north parts of MS and AL or TN. There are common threads that tie the South together, but every area, even in the same state, has its own flavor. The central gulf coast has a lot more seafood than inland (where venison and freshwater fish are more common) and a strong French influence. But there is still a lot of fried foods, sweet tea, cornbread and grits. That's why I would recommend carefully researching areas before opening a restaurant. The same Greek pizza could be wildly popular in one town, but a complete failure elsewhere.