I've always thought that the nicest time to spend in the French Quarter is a weekday morning. The craziness of the night is (mostly) gone, there are far fewer tourists or people in general on the streets, and the morning sun highlights the area in a way that you don't see later in the day. Mornings make the Quarter feel like a real neighborhood with a history that you can almost taste. I was in New Orleans for a job a couple weeks ago, over a weekend. My flight on Monday wasn't until the afternoon so I was able to spend the morning just wandering about.