www.neworleansonline.com is a great site for ideas. Self-guided walking tour maps, listings, even discount coupons you can print out. You can also order their free guidebook to be mailed to you, but all the guidebook info is on their web site as well.
The French Quarter is fairly compact and you'll be able to walk everywhere within it. Then venture out to the Garden District if you have the time. Lots to see and do there as well.
The one and only "must do" for me is Beignets at Cafe Du Monde. Everything else is just icing on the cake.
New Orleans is my favorite city in the United States, primarily for the French Quarter.