There's Canal Place, which has upscale shops (pricy), but you can shop at those anywhere. The absolute best way to do it is just grab a map and wander around the Quarter- the best shops are little hole-in-the wall boutiques or galleries. Kruz is an excellent ethnic boutique right near Esplanade that I would highly recommend- lots of good stuff. Bourbon French parfumerie has some of the prettiest antique and Venetian glass perfume bottles and accessories (think detailed little decanters and atomizers, compacts, etc.) as well as their own line of perfumes; I think they can mix custom scents for you as well. Another custom parfumerie is Hove parfumers; it's also in the quarter- if you're looking for unique scents, try them both and compare. There are a lot of great secondhand stores if you like thrifting; Paisley Babylon is a good start. Check out the French Market- the front has fruits/vegetables and local cuisine (alligator on a stick- yum!), and there's nothing like buying a big hunk of sugarcane and just eating it right there on the curb. Same goes for watermelon, satsumas, etc. It's a very informal market, and has the typical touristy stuff, but also has some great local crafts, jewelry, etc. if you take the time to look around. The back part is all vendor tables- definitely worth a walk through, and it's historic to boot. Try the Fauberg Marigny behind Esplanade- start on Frenchman and check out the little stores, galleries, etc. Some new restaurants there, good food, fantastic little gay and lesbian bookstore with an excellent selection if you've got an open mind and like to read. You could have your cards or tea leaves read at the Tea room (on Chartres); it's a short walk from Jackson square. Or, take your chances with the square vendors and have them read right there on the sidewalk- though I'd recommend the Tea room. Have a gelato or some spumoni at Angelo Brocato's- their pistachio ice cream is the creamiest, most delicious thing known to man. Take a cab to Magazine Street and spend an afternoon walking around, antiquing, etc. If you're into alternative music, try the Mushroom on Broadway. Their employees are virtual music encyclopedias, and it's a great place to get recommendations on new music, both national and local (particularly local). Speaking of local music, try Louisiana Music Factory (they often have live in-store performances with local musicians; check the listings) or Tower records, which is a chain but has a FANTASTIC local selection. Get a burger (the biggest and best IMO) at Port-of-Call on Esplanade. Go to the Voodoo Museum (Dumaine). Ditto on the pharmacy museum (it's really, really worth it, and it's really, really cheap!) on Chartres. Grab a Gambit Weekly when you get into town (they have them at all Barnes and Nobles, and most people can tell you where to get one if you can't get to the bookstore) and an OffBeat! magazine (lists EVERY bar and club with all music acts- both of these are free publications) and read through them for more ideas. Let me know if you need any more info.
Oh, and Carmelo's Ristorante Italiano is on...South Peters?...right by the river, and it's some of the most delicious Italian food you've ever eaten. I could type forty pages about the food alone, but if you're looking for the best of the best, I recommend Carmelo's, Port-of-Call, the Gumbo Shop, and Court of Two Sisters. All right there in the French Quarter. Have fun!