Savanna bay on Virgin Gorda is one of my favorites, and usually not crowded as most people don't see how to get in. It may be marked as off limits from the charter companies, but the first 5 years I chartered I went in and have been going since in my own boat.
go into google earth and put the coordinates of 18.28.00.94N 64.25.37.00W and it will take you right to the entrance of the bay. Go in between 10am and 1pm on a sunny day so you see the cut. it's about 50 feet wide. stay an equal distance off the shore and you'll be in approx 15 feet of water. there will be 3 coral heads after you enter in (they show up on google) that are easily avoided as they show up really dark in the water. once past them, stay in the darker water and find a point off the beach you like. slowly go in and anchor in about 10 feet of water to avoid too much bounce from any northerly swells. if you have east, NE, SE winds, it will be calm and wonderful for overnight.