Hmmm only 5-6 hours in NO, my first inclination is to suggest you just eat your way across the city; but I guess since it's your husband's first visit a few must sees are in order. I agree Cafe du Monde and Pat O'Brien's are musts, but unless it's raining don't stay inside, instead head outdoors and enjoy your beignets and coffee on a bench near General Jackson, and definitely get your hurricanes in "to go" cups, "lub..ri..cate" your stroll through the Quarter... very smooth. (Don't worry it's not a crime to walk in the Quarter with a drink, as long as it's in plastic)
Definitely stop in some of the more unique shops in the Quarter, from voodoo to hot sauce shops you can find almost anything there. Oh, I do recommend taking a few bottles of hot sauce home, trust me, no matter how many times you ask, your local store is never going to carry "ass kickin' original cajun hot sauce", just not enough demand.
Definately walk over to RiverWalk. You can take a riverboat cruise (personally I'm not one for boats), or visit The Aquarium of the Americas.

Restaurants--I like Ralph and Kacoo's, 519 Toulouse, in the French Quarter. Ralph & Kacoo's
My menu favorites the gumbo and the etouffee, the oyster bar is good too.
Pralines--Southern Candymakers, 334 Decatur St., there's another on Jefferson, trust me fresh is better, definately take some home.

Outside the Quarter
Garden District--If you get a chance take the St Charles streetcar out to the garden district, walk the streets and get the streetcar back. Just remember that it's public transportation, so no commentary and you must have exact fare.
National D-Day Museum- the staff recommends you allow at least 3 hours to see the museum.
National D-Day Museum

A drive away
The cemeteries. But take a tour, it's just not safe to go wandering, thieves NOT ghosts.

I think that should keep you moving. Also read my New Orleans trip report for a few more ideas.
If I can be of more help, just let me know.

A great New Orleans site New Orleans vistor's guide

Keep'em flying