A Muffaletta is a New Orleans classic, a Po'-Boy sandwich that includes olive salad (that unfortunately won't appeal to olive-hating Kathy). Napoleon House makes a USA Today article about sandwiches, while Bobby Flay extols Serio's and urbanspoon likes Central Grocery.
As to beignets, those square pieces of sugar-topped deep-fried dough, there are just as many choices. Café Beignet and Café du Monde come up in searches.
We haven't even begun to think about dinner.
Not to worry though. Kathy's brothers will have done the scouting - they've visited The Big Easy previously - and we'll relax and enjoy the results of their research.