Long weekend in New Orleans...
Around when are you planning on coming? There's always some sort of festival going on and many are centered around food, so knowing a date would help. For instance, June 13 - 15 is the creole tomato festival and the seafood festival is June 7-8.
I second many of the recommendations above. I would also like to add in MiLa, a newish restaurant located in the CBD. (milaneworleans.com) It's southern and local classics made with locally sourced fare.
Also, you might want to check out Bacchanal. (bacchanalwine.com). It's a great wine shop in the Bywater with a courtyard out back. On Sunday afternoons, there's a local chef serving up delicious food for ridiculously cheap prices. And you can just buy a bottle or two of wine and get some glasses from inside. It's a great way to wrap up a weekend.
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