Willa Jeans, Ruby Slipper and Red Gravy are all in/near the CBD and are good/popular for both breakfast and lunch.
Drinks? In New Orleans? Surely, you jest!
One of my favorite spots is Johnny Sanchez. It's a John Besh & Arron Sanchez collaboration. Nice space, great happy hour. Voodoo Two and The Sazarac Bar at the Roosevelt Hotel are both nearby. Walk-Ons is a sports bar with typical bad sports bar food, but it's popular. The Little Gem has a bar downstairs and another space upstairs. Music both up and down, depending on the night.
These are all an easy walk from where you're staying. There are millions more options around town, depending on how far out you want to go.