Café du Monde
The obvious answer, handled honestly: get there at 6am and it is wonderful.
French Quarter
The canonical pick. Beignets and chicory café au lait, open 24 hours, in operation since 1862 in the same spot at the French Market. The trick is timing — 9am to 11pm is overrun with families and tour groups, midnight after a show is empty and lovely, 6am at sunrise with the cathedral bells across Jackson Square is the secret most visitors never figure out.
Three beignets per order, served hot, dusted in powdered sugar that gets everywhere. Wear something dark that hides it or accept that you'll wear a little of New Orleans home. Cash speeds the line; card works at the table. The original location is the only one worth bothering with — the airport and mall outposts are not the same thing.
Don't believe anyone who tells you Café Beignet on Royal is better. It isn't, but it's a respectable backup if the line at Du Monde looks like work.
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