Fun! I went a few years ago with my Mom and this is what we did in about two days:
Guided walking tour of the French Quarter (probably too much walking for your sm, but maybe they do carriage or other style tours).
Toured the Cabildo (State Historic Museum). It's in Jackson square and at the time had exhibits on Mardi Gras and Katrina (talk about contrast).
Found places to eat gumbo and oysters and did Cafe Du Monde.
Rode a trolley to the Garden district, then explored a cemetary followed by A martini lunch at Comanders Palace (locals told us to ask to be seated in the garden room).
Jazz music at Preservation Hall (so much fun, but you do have to stand in line for tickets, so maybe not the best for your sm).
Demo cooking class at New Orleans Cooking Experience (not to be confused with New Orleans Cooking School). It's in a historic house and at the end you all eat around the dinning table. It will be mostly locals, so a good chance to learn about the city.
Drank sazaracs at the Roosevelt hotel.
There you have it. It was a fun, tame way to see New Orleans. The WWII museum is supposed to be excellent, but is farther afield. Just eat lots of good food and you are sure to have a good time!