First, bring an umbrella, and shoes that you can get wet. Tell your wife that high heeled sandals can be a problem in the rain, just be prepared.
Second, do not put anything into your mouth that isn't great. Food is a religion in N.O. and it is just too sad to ruin your chance at a good snack by having some ordinary breakfast at the hotel. Some of the best visits I've had included stopping at great restaurants mid-day for an appetizer, a cup of turtle soup with sherry and a little oysters au gratin. Ask in the shops for someone who lives in the area to recommend for a good place for a lunch, many of the places that you wouldn't think are good, they look too seedy with strange creepy people, are actually better restaurants than the "big names" for a fraction of the price! Do not let paper napkins and those tatooed guys drinking at the bar at 3 PM keep you from a great meal.
Thrid, pack pants with elastic waistbands. You will put on 1 to 2 lbs a day. More if you drink, maybe less if you dance.
The shops in the Quarter are interesting, a carriage ride as suggested is great, shop a bit for the best story teller/historian driver. Bourbon St. is not the whole Quarter, visit Royal St. and go down to the Farmers Market. Be sure to have Beignets at the cafe across from Jackson Square (do not wear black and don't exhale as you bite a beinet). Maybe visit the museum in the Cabildo there, they did have a great exhibit on Jefferson's purchae of Louisiana, might be there still.
Ride the streetcars down St. Charles Ave to see the mansions, step off in front of Tulane Univeristy (and Loyola Univeristy right next door) to go to Audubon Park and see the big Live Oaks. The zoo in the park is good if you have kids.
Only a day, skip the swamp tours, but consider a Ghost Tour or somthing like that.
Find some good music, Preservation Hall, or Blues Cafe sort of place. The second religion of N.O. is music.
Last, watch your back! It is not a safe area. Do not be drinking enough to be unaware of your surroundings. When in doubt, hail a cab. The nicest areas of N.O are right next to the highest poverty. I don't worry about pick pockets (although in the crowds of the farmers market there are pickpockets) as much as out and out muggers who'll shot you.
I grew up ratting the streets of the Quarter, how my parent's let me go down there so much I don't know, oh, wait, they had no idea that's where I was. I saw some strange stuff and got into some close scrapes there. It can get pretty weird there sometimes.