I will be visiting this resort for the first time at the end of June. I have some friends that live there and have made some recommendations.
www.freetoursbyfoot.com offers free walking tours of the Garden District, French Quarter, Cemetaries, etc. These are two-hour tours and you just tip them what you feel it was worth (from what I researched from $10-$20, mainly $20). Mardi Gras World--they offer free pickup at various hotels. Oak Alley Plantation and the Laura House Plantation. Swamp tours. Take the St. Charles Street Car to view beautiful houses. Carriage rides around the quarter offer a lot of history. In the French Quarter there are many historic homes to tour: The 1850 House, Beauregard-Keyes House, Gallier House, Hermann Grima House. If you like museum--The Cabildo (one of the most historically significant building in America). The National World War II Museum. For music, the locals go to Frenchman Street. For shopping, Magazine Street (the best stretch is from Jackson to Louisiana).
IMPORTANT: If you are touring the cemeteries by yourself, please be cautious. There has been reported thieves. Also, the French Quarter is not the safest place. Don't go wandering around out at night by yourself. Stick to streets that are populated--not on the outskirts. You will know when you stop seeing people.