you won't get the best of nola eats that late (save fine dining for daylight hours or dinnertime), but at that point you'll prob be ready to eat your arm and there are plenty of late-night options.
if you just want to scarf something down before you grab a seat at a 1-2 table, there is a Lucky Dog stand literally next to the poker room, and you can get a giant dog loaded and a bag of chips for about 8 bucks. the Fudrucker's in Harrah's also usually stays open late, so could get a burger. i usually say stay away from chains in nola, but if you just need a quick bite so you can start degen-ing, it's an option.
other than that, you'll have to venture outside of the casino. the camellia grill is a new orleans legend, corner of Chartres and Toulouse, it's a diner. not 100% sure they're open 24/7, but i think they are. it's about a 10 minute walk from casino.
clover grill is DEFINITELY open 24/7, same diner vibe as camellia, though maybe a little sketchier, in a good way. it's about a 12-15 walk from casino, corner of bourbon and dumaine.
neither camellia nor clover are 4-star cuisine by a long shot, but it's good greasy diner food and both are new orleans institutions that you'll probably get a story or two out of.
if all else fails, go to bourbon street, ~5 minute walk from casino, where there's a place selling pizza by the slice on about every other corner. for 5-10 bucks you can fill up on greasy pizza goodness and then you'll be ready to get back to the casino...or pop into some other establishment in the area