The best that I have ever found was at the Carousel Bar at the Hotel Monteleone. Now, I do not know if the Carousel Bar is still there, or if they are as good, but back when, they were great and unique.
I just got back from Jazz Fest and have to tell you, I still love Cafe Lafitte in Exile's bloodys. Get a double with a whole garden of yummy snacks to take with for brunch at Eat (one block away) where you must order the Shrimp and Grits bowl.
I don't know if a drink is reason enough to pay for a meal, but the bloody at Galatoire's is outstanding. Otherwise, I would trust any libation from Antoine's Hermes Bar, everything we have had there has been great.