Definitely go to Cooper Island, totally unspoiled and a very nice restaurant there, about 20 moorings so get there early.
Also go to the William Thornton its a boat / restaurant at Norman Island - very cool and great chicken wings!
Pussers - tavern on Tortola just off main street. very nice for lunch.
Virgin Gorda - The Baths and Devils Bay are incredible
The Dogs - 3 islands - great snorkeling and they sank an airplane there (purposely) which u can go in!
Peter Island is very smart - probs the nicest beach there is! but restaurant is v expensive.
Have fun!!!! it is incredible out there.
(hoping to go back for my gap year!)