I've been to NO several times, twice just last year. We were there for New Years Eve and were planning on going back this Thanksgiving.
I love that city and its a great city. Like many places it has its bad and its good, but its good is VERY good.
When this is all over, and the city is back on its feet, my wife and I will be the first to start pouring money back into the city.
Needless to say, Mardi Gras either won't happen this year, or will take on a new meaning.
That's true of most cities that seem to have a "bad" reputation among rural residents: New Orleans, New York, San Francisco, Las Vegas. I've found the good in all of those places far outweighs the bad, and the bad is no reason to stay away. Just be alert, study maps and know where the bad neighborhoods are before you get there, and don't do silly things you wouldn't do at home (the main reason that tourists get into trouble).
Cities attract the best and the worst of humanity. To experience the best, you have to be willing to tolerate a little bit of the worst.