Since quite a few of us are going to be looking for it, let's post which islands we've visited and any information we've collected, such as whether the island has a waterfall, or a locked entrance to something below the surface, or both. If an island definitely doesn't contain the Tavern, post that. If you're not sure, post that too. The biggest islands are the most likely. I've heard a few people talking about Thieves' Haven as a potential spot, but any of the large islands can also work.
Happy hunting!