I, too, would still go to New Orleans. There is so much to do and we stayed at the French Quarter RV park back in 2008. That was three years after Hurricane Katrina. The city was slow coming back but was still a lot of fun.
Like in any city, you have to keep your eyes open and be aware of your surroundings. We took a tour down the River Road looking at the Plantation houses and actually stayed at 'Madewood Plantation' one night as it is a B & B. It was a lot fun.
Go on the trip and be careful like you would anywhere.
MM.