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Green beach is on the west end of Vieques.
It is extremely remote and has no significant facilities except for a gazebo or two. In prevailing conditions this area is quite calm, though one caveat is that I've only visited in a large cat (3 times), so YMMV if you're in a monohull.

Anchor south of Punta Arenas off the gazebos (or off the small rocky breakwater) in about 10-15 feet of water. You can dingy in or take you water toys in and explore the beach up to and even around the point. Sometimes you will see locals here, but often you'll have the whole place to yourself, particularly after 4pm.