Hip little café a block or so off of Bourbon on Conti (of course). We enjoyed this place so much we ate here 3 out of the 4 mornings we were in New Orleans. I think the prerequisites to work here are; be young, hip & very soft spoken. Come here for the food and don't expect much in the way of service. Once they've taken your order, you will not be attended to again until they serve you your food (unless you ask, of course). Obviously, this didn't dissuade us from returning.
The lox & bagels are wonderful as are any of the Benedict dishes. They serve breakfast, brunch and I presume lunch, closing at 3 pm. I would highly recommend as a quick & less expensive alternative to some of the other brunch spots in the French Quarter. One note: if you're looking for champagne or other alcoholic drink with your brunch, you'll have to look elsewhere.
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