Hey, I'm right outside of NOLA in Metairie.
I have not been able to find much in the way of paleo friendly shopping with the exception of Whole Foods. There is a little farmer's market in Hollygrove-but I have never been because it is a REALLY dangerous area.
There are also smaller markets held once or twice a week around the city.
Where in NOLA are you moving? If you are closer to the quarter I am sure there are more options.
Also make sure to check out some of the restaurants down Magazine street. There are some great places to grab a casual dinner and great bars to get a drink afterwards. One of my favorites is St. Joe's. The have the best blueberry mojito in the city.