The Lafayette Cemetery is very old and very beautiful. Although not maintained as well as some of the bigger New Orleans cemeteries, Lafayette offers the perfect photo opportunities: old stones, angels, rustic views, lots of wrought iron. The dates go back to the mid-1800s. You can go there on your own, or with a tour. Only blocks away from the St. Charles Street Trolley (a very fun ride to the Garden District).
FYI: Lafayette is the cemetery Anne Rice features in her Vampire Chronicles.