Only a few hours in NOLA, my first thought is to tell you to just eat your way across the city.
Although I've never taken the airport shuttle, I think M767 has a good idea, taking the shuttle into the Quarter seems like the way to go.
Now it's time to eat-
Like Nick said, first stop Cafe du Monde for beignets and chicory coffee, just don't wear black. Then explore Jackson Square, (it's right across the street) and visit St Louis Cathedral. Then hit the shops in the Quarter, as Nick said there are lots of antique shops, but I like the voodoo and hot sauce shops. The Quarter is not all that big, so you'll have time to take in some music and don't forget to get a hurricane at Pat O'Brien's -they say Pat invented the drink, but who knows.

You can also walk over to Canal St and catch the street car, it passes through the Garden Distict. (must have exact fare) New Orleans Streetcars

Pralines--There are lots of places selling pralines down there. But I like Southern Candymakers 334 Decatur St., on the edge of the Quarter.
Personally I think fresh pralines are the only way to go.

Food-
K-Paul's 416 Charles St. in the Quarter is good. But there are a lot of tourtists, and I think it's a little expensive.
I love Ralph & Kacoo's 519 Toulouse St, near the riverboat landing. (crawfish etoufee-MMMMM) Eat there everytime I visit.

Have fun and don't forget your shrimp po'boy for the flight home