If you're down on Bourbon St, it's mainly BMC. However, there is one spot (actually 2 as they have 2 locations) called Beerfest. They've got about 50 beers on tap and some of them are out of the way micros (although most are very commercial micros).
The beer is expensive (welcome to tourist central) but they have a way to get discounts. Women can trade their bras for beer. No nudity required, but you have to take it off on the spot. It's brilliant!
On a serious note, if you are on Bourbon and you want good beer, it's your only choice.