How convenient is it to go from the Andaz Mayakoba to Cozumel for a day trip, or to Tulum?

Would you rather stay at the Intercontinental on Cozumel or the GH PDC or the Andaz Mayakoba?

Sounds like for snorkeling and natural beach beauty - Cozumel is supposed to be good?
Sounds like for convenience/nightlife/people watching/shopping/strolling - with less natural beach beauty, and everything being a little more crammed in - Playa Del Carmen fits the bill
Sounds like the Andaz isn't in either Cozumel or PDC, but north PDC. i wonder if I will find myself discouraged by the long distances to get to PDC/Cozumel/Tulum from the Andaz? But on the other hand, I also wonder if the pool at the Playa Del Carmen is way undersized.

My initial thought; spend 3 nights at the Andaz or PDC, and then spend 2 nights at the Intercontinental Cozumel. But I am not sure what will be the best combo...

Any thoughts?