This coffeeshop on Decatur Street in the French Quarter is a New Orleans institution. The cafe is open 24 hours a day 364 days a year (it's closed on Christmas). Personally, I'm not a coffee drinker, but this coffee has chickory in it, which makes it quite different. Don't drink too fast as the coffee is normally very hot when it arrives at your table. Be sure to order some beignets (squares of dough that are fried and covered with powdered sugar); a serving is three beignets.
Across the road from the café is the Café du Monde store, where you can buy the coffees, beignet mixes, and other little delights, including my favorite, fudge; the coffee and vanilla fudges are a treat for any sweet tooth.
It can get very busy, so chances are you'll have to stand in line. Also keep in mind that they dont really have a menu, there are no entrees and appetizers, its pretty much just coffee and beignets.