St John USVI would definetely fit your bill, many villas to rent, best from the beach snorkeling and 2/3 of it is national park.

BVI is similar too, but may not be the extent of biking and hiking as you would definetely get in St John. Plus no worries about passports if you do not already have. see destinationstjohn; caribbean villas.com for some choices of vacation homes.