Morning Call's beignets have always been better than Cafe du Monde's. They used to be located next door, in the market on Decatur, but after 104 years in that spot got tired of tourists and in 1974 moved to Metairie. Back in the day when I flew down to NOLA often I always made it my first stop into and last out of New Orleans.
1) Cracked conch at The Conch Shack, Blue Hills, Provo, Turks & Caicos
2) Chiles en nogada in Puebla, MX, in Sept-Oct (now!) when every restaurant is competing to offer the best.
3) Unlimited oysters diving from Margarita Island, off the Venezuela coast. We bring limes and hot sauce and have a shucking feast after the second dive. Columbus' best bounty to Isabella was 320 pounds of pearls from Margarita, which is greek for pearl
EDIT: I would be derelict not to include stone crabs at Joes (or elsewhere), the season begins in 33 days!