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.
These are great recommendations. Hit them all on my last trip. I'd also recommend the bars at Restaurant August and The Polo Club Lounge in the Windsor Court Hotel for pre dinner cocktails.