@RobertSimonson made a survey.
I think the Mai Kai should be number 11, but otherwise, this is the list as far as I know. I can think of at least a smattering of additional “iconic” cocktail bars, but in each case, I can see how they are not on the same tier.
I find it a bit depressing that only three of the ten—or rather, four of the eleven, in my opinion—are in the United States, and I find it a bit irritating that Hemingway’s imprimatur looms so large. But those are the facts.