Stay away from Bourbon street it is a tourist trap. locals don't go there.
For Jazz go to Snug Harbor.  
A really good restaurant is Feelings Cafe.
Good place for lunch is the Napoleon House.
Good place for burgers is Port o call. (this is especially good place for hangover food)
The Columns Hotel on St Charles has a great bar.
Go to the Sazerac bar in the Roosevelt Hotel and get a Sazerac cocktail.
I think another good bar was the Mayfair.
I have been to a lot of good bars there, but the names and locations are fuzzy.  Usually I get a hangover for every day that I am down there.  Sometimes I even see the sun come up