Hang out at Cafe du Monde eating beignets, sipping coffee, and watching all the people go by. Visit the aquarium. Go shopping in the Quarter. Go to restaurants and clubs in Faubourg Marigny.
Quick Tips:
Don't visit if you're on a diet.
Best Way To Get Around:
Everything in the Quarter is within walking distance and you're relatively safe at all hours (common sense should always prevail). If your feet get tired, there are plenty of taxis (especially near the numerous hotels) that are not too expensive.
If you plan to venture into the Garden District or go shopping on Magazine St., you can take the street car. I would take a taxi at night since this area can be a little dicey at night.
Parking could get tricky, so I wouldn't advise renting a car.