I haven't made it into this exclusive club, so I can only relay the details I've heard, just so you'll know what you're missing.
In the French Quarter, on the top floor of the building that houses the Blue Bayou restaurant, you can look up and see some delicately shuttered windows. Behind those windows, with a view of the water, is the Club 33 restaurant.
To get in takes a membership that is supposed to be expensive, like $20,000, with a three-year waiting list. Also, supposedly, this is where all the famous dine when visiting the park, people like Michael Jackson and Liz Taylor, who are supposed to be members.
I can imagine corporations writing off a membership here to impress clients, so all this may be true but, so far as my prospects for ever dining there, it's all just supposition.