New Orleans has one of the strongest food cultures in the United States — arguably the strongest, given the depth of the Creole and Cajun traditions and the city's history of absorbing influences from France, Spain, West Africa, and the Caribbean. Eating well here is not difficult; eating badly requires some effort.
The extremes are both worth experiencing. Antoine's, founded in 1840, invented Oysters Rockefeller and Pompano en Papillote and has been refining both ever since. Commander's Palace in the Garden District is the training ground for the city's great chefs and serves the best formal Creole meal you will have anywhere. At the other end of the register, the po'boy — a fried oyster or roast beef sandwich on local French bread — is the working lunch of New Orleans and best consumed standing at a neighbourhood counter. The Central Grocery on Decatur Street invented the muffuletta (a round Italian sandwich with olive salad) in 1906 and is still making them.
The food to eat here is not generic: it is Creole. Red beans and rice on Mondays (a tradition so old that Louis Armstrong signed his letters "Red beans and ricely yours"), gumbo, jambalaya, crawfish étouffée, bread pudding with whiskey sauce.