New Orleans is the birthplace of jazz. Music can be heard everywhere, from street perforamances, to smoky clubs to giant concert halls. For pure jazz, head to the Frenchmen St. as I found Burbon St. extrelemely touristy.
Across the street is the Spottet Cat, where the atmosphere is a little more spicy; there is not sitting or dinner service here just dancing in a packed bar with lots of like-minded jazz lovers.
There is no place in the world for live music like New Orleans! A must, if it's in your bucket list!