I was there in late Feb - early March, heres some of the places I went to.
-Beignet & Cafe Au Lait @ Cafe Du Monde on Decatur right accross Jackson Square, French Quarter
-Gumbo @ the Gumbo Shop on St. Peter St, French Quarter
-Blackened Catfish @ K Pauls Louisiana Kitchen, can't find address but it should be somewhere near Burbon St.
-Great breakfasts @ Madelains (sp?), a small chain bakery, should be easy to find.
-Never been but I hear great things of the Commander's Palace, 1403 Washington, Garden District
-Red Fish on 115 Boubon St, French Quarter...this place wasn't bad though a little pricey for what you get.
I'm looking through www.neworleans.com
but I can barely find half the places I visited. I found most of these places just by walking around the French Quarter and around my hotel, Le Cirque by Lee Circle.
Things you have to see though, the Laffayet Cemetary, St Joseph Cathedral, Riverwalk mall, a swamp tour...this place is nightlife central. Check out Burbon St once the sun sets! You'll enjoy yourself, believe me.