atmospheric patio dining in french quarter/marigny for lunch?
Maison deVille has a lovely courtyard. It's less than one block off Bourbon and is part of a hotel. If you stay into the early evening, you could have dinner there, too.
The Marigny Brasserie doesn't have a courtyard, but is good with a nice wine list.
A different atmosphere is the restaurant at the top of the Marriott on Canal. The waiters don't mind if you sit and drink there. You can see most of New Orleans from their vantage point.