We ate a cheap/quick lunch at Dat Dog while down there, they had all different styles, and they were delicious. Yes there are lots of fine dining choices, but we loved Dat Dog. Willie Mae's Scotch House came highly recommended, but we decided to walk there and it was in a sketch neighborhood and closed right before we got there, but it smelled delicious.
We ate breakfast at Cafe Beignet and liked it a lot more than Du Monde.
We spent three or four hours at the WWII museum (I'm a Germany fan, and a history teacher so I was enamored). I could have easily spent more time there, but my long-suffering wife was ready to go.
Sorry that I can't recommend nicer places to go or see, we like to see the highlights and some local places generally when we travel. NOLA is definitely on our must return list.
We also had Hilton points galore and wanted to walk everywhere, so we stayed in the Roosevelt. It was a fantastic place, and they claim to be the home of the first cocktail. Our stay featured 2 free drinks at their bar, which was pretty nice.