The antique stores are great, IMHO. There are some awesome and unique places, like Cohen and Sons, for antique weapons and currency, and some great antique/vintage watch and clock shops. The real benefit to shopping in New Orleans is in old stuff that you can't get everywhere. NO can't ever compete with NYC for new and shiny, but nobody does old and patinated like the Crescent City.
I was once at Couronne Jewelry and Watches looking at a gorgeous NOS Zenith El Primero, talking to the owner about how his dad got piles of them when Zenith TV and Zenith watches were under the same corporate umbrella. After we'd been talking awhile, he showed me drawings of a watch he was planning to produce himself. It was cool to see the press releases and photos for New Orleans Watch Co when he had them produced. That sort of thing happens there, and it's cool.
One other gem in New Orleans that's not to be missed is Meyer the Hatter. It's just outside the Quarter, but it's a must-visit. Sam Meyer has been selling hats since he got back from WW2, and has designed at least one model by Stetson. They're on their third or fourth generation of Meyers running the store, and apparently get an impressive amount of celebrity traffic. I wrote a blog post about my visit there: http://www.completesoutherngentleman.com/stetson-gulfport-hat-by-meyer-the-hatter-new-orleans/
Hope you have a good time!