I like the combination of a great view and great music...Le Plage on St. Jean Bay in St. Bart's and the Dune Preserve on Anguilla are among my favourites for these reasons.

This joint is a little bit of everything but it easily fits the qualifications (I think being a 'dive' helps as well). http://www.divemontserrat.com/

Although not on the Beach, but on the hill above the 4B's (Bunkum Bay Beach Bar) in Montserrat is also quite a joint.