For gumbo, search for "gumbo z'herbes". Traditionally we eat it during Lent (specifically Good Friday). Dooky Chase was previously one of the few places to get it, but I believe that it's been closed (I left the country a few days after Katrina hit [a planned leave, as I was moving for work] and only go back once a year so don't get to check out all but my favorite restaurants then).
Some restaurants to definitely check out (all of these are downtown):
Herbsaint (don't forget to try its namesake, herbsaint, New Orleans' own pastis): 701 St Charles Ave (by Girod)
Galatoire's (make sure that your husband brings a jacket, but keep in mind that you may have to wait in line): 209 Bourbon St (by Iberville) -- try their turtle soup and the NOLA traditional cafe brulot
Brennan's: 417 Royal St (by Conti) -- try their seafood and okra gumbo, as well as the NOLA milk punch (but perhaps they're best known for bananas Foster
If you're going to head toward City Park/the Museum, you could instead check out Ralph's on the Park (900 City Park Ave), another of the Brennan family restaurants. (My friends in the neighborhood would want me to preface this by asking you to please not sit on their front steps.)
Most of these have been Creole food (being a Creole myself, I'm partial ;P), but for Cajun food, if you're not going to head into Acadiana, you could always try out Mulate's (not my favorite for Cajun food, as it is a more middle Acadiana style than the Acadiana Coast style of my Cajun relatives that I prefer, but it is decent), located at 201 Julia St (by Convention Center Blvd). Their gumbo is very different, with a dark roux and poultry and seafood together, characteristic of the area. That said, their ecrevisses (crawfish) a l'etouffee is quite decent, as are their cuisses de grenouille.
It's good that you'll be down there after August, as that's when most of the city restaurants close for the summer. It's far too miserable to be in NOLA in August (and, oh, how I hated waiting tables then!). Dresses are best, as are comfortable sandals. However, if you wish to go to nicer restaurants, a cardigan for yourself and trousers + jacket for your husband may be necessary.
