Eat some king cake. Eat all the king cake. Eat oysters. Have a roast beef po-boy. Start drinking in the morning with an “eye-opener” like a mimosa or Bloody Mary. The Gumbo Shop has good gumbo and killer bread pudding.
You’ve managed to pick the one weekend during Mardi Gras where there are no (official) parades. Craziness will still be happening in the French Quarter, though.
Stay in the tourist areas of the French Quarter! If you find yourself suddenly alone on the street, even in a tourist area, turn around and go back the way you came. Just be aware of your surroundings in general. I’m not trying to scare you, but tourists are easy pickings.
Try one of the Haunted History Tours. I had in a friend in from out of town and she talked me into going with her. It was a lot of fun and I learned new stuff! If you can get a voodoo tour with Bloody Mary, do it! She’s a lot of fun.
The National World War II Museum is top notch. Go to Frenchmen Street for live music. You can pretty much walk around until you hear something you like. The New Orleans Museum of Art has a really neat sculpture garden.
Welcome, and have fun!