Agree with XRayMan on Leverick-always our favorite for food.
Brandywine on Tortola is another good suggestion.

If you want to have a place to yourselves check out the Bistro at Blunder Bay. We are almost always the only ones there. I am not sure I would call it the most romantic place but the views are great and if private is what you are after it fits the bill. Food has always been good and they aim to please.

Check out little Dix Bay as well.

Or you could go in a different direction and hire a private chef.