Here's two case studies for you involving two different individuals: myself and a friend of mine who graduated at the same time, same year, same age.
I moved to TN to be with my then-GF/now-fiance who is in grad school. I was out of work for a few months, but I ended up with a pretty great job that I enjoy a lot, although it wasn't what I had in mind coming out of school, its kind of related but still fun, even though I don't make a ton of money. What I did do, though, is get away from home, have a lot of fun meeting new people, had new experiences, and got to do something different at a time when a lot of my friends are starting to settle down in the same zip code where they grew up.
My friend decided to take a paper-pushing Dept. of Labor job back at home. He lives with his parents, hangs out with other high school friends who never left town, and generally is fairly miserable. He did, though, pay off his student loans and has traveled quite a bit. He's 27, has no debt, and a Master's.
To sum up, you're basically in a win-win situation. It depends on what your long term priorities are. Getting a job in your career field with a great salary is HUGE, and you probably won't realize how important and necessary that is for a few more years. However, moving to NOLA, living in the heart of the city, and having fun is what being in your 20s is all about. I have zero regrets about moving away and taking a lower paying job. I could have stayed at home and paid off my loans while working a job I didn't like, but that's the tradeoff.