The main area for nightlife in New Orleans is the French Quarter, particularly along Bourbon Street, where you can find anything from quiet candle lit bars such as Lafitte's Blacksmith Shop (allegedly the oldest bar in the USA) to wild strip joints (at the western end), to lively jazz bars.
The city prides itself as the home of jazz music, and there are many places to go and listen to it, highly recommended is Storyville District - one of the top bars in the city, where there are several stages showcasing different musicians, as well as a fine restaurant.
If you've had enough of the bebop, and want to listen to something a bit more contemporary than jazz, then Ampersand in the centre of the city is an upmarket club that attracts the younger New Orleans clubbers with a mix of techno and house music.