Don't get me wrong, there are many great bars here. Dean, I think the Avenue Pub is the bar on St. Charles you are referring to. And yes, I credit the Sazerac bar with reinstilling interest in the eponymous cocktail. Before the Roosevelt opened its renovated doors, it was hard to find any bartender in NOLA that could make a decent one.
I haven't tried the Bourbon House yet, but after finding this link on their website, and seeing the banner image at top, I think I'll have to swing by:
http://bourbonhouse.com/bourbon.html
I'd also recommend a few other places to potential visitors:
Bar Tonique - Great cocktails on the edge of the Quarter
DBA - Frenchman St., very good whiskey selection and live music
The Cure - Great cocktails, whiskey, and small plates.
Napoleon House - Classic New Orleans bar & restaurant. Nothing fancy, but I still love to go here on a summer afternoon and knock back a few. Had my first Sazerac here, and I still think they make them the best in town, although it has to be made by a specific bartender.