Not much near the French Quarter at the moment. Crescent City Brewhouse and Gordon Biersch are it right there at the moment. I highly recommend GB though. The brewer is given a lot of latitude for experimental stuff besides doing a great job on the regular lineup. Nice guy too if you get a chance to chat. His name is Sonny Day.
That being said, there are several beer spots and breweries that you should try to get to.
1) The Avenue Pub - In my opinion, it's the best beer bar in the gulf south. Good whiskey selection too. It's on St. Charles Avenue, so you can get on the St. Charles street car at the corner of Canal and Carondelet. Get a day pass for $3 a person. The Avenue is at the corner of St. Charles and Polymnia.
2) NOLA Brewing - On Tchopitoulas by the 7th Street Wharf. Really nice 2 story tap room. Friday tours are from 2-4 featuring free beer.
3) Courtyard Brewery - Small scale brewery serving their own beer and lots of guest stuff. Scott's from San Diego originally, so he brews a lot of hoppy stuff, but has some other stuff from time to time.
4) Urban South - Just opened officially. Right now they have an IPA and a Wit on.
Shameless plug of a friend's article:http://www.nolabeerblog.com/p/up-to-date-list-of-all-louisiana.html