I don't know about any Scottish places, but it would be a shame to visit New Orleans without stopping by Cafe du Monde. It's on Decatur Street at Jackson Square. It's the oldest coffee house in New Orleans and they have the best beignets and coffee with roasted chicory. They're open 24/7, so after all the New Year festivities and drinks, the cafe will be super busy. Oh, people run small businesses out of their parlors on Burbon Street so keep an eye open for interesting stuff. Last time I went I found a woman offering 10 minute foot massages for $5.