St. Thomas: Old Stone Farmhouse, Easterly, Prime
St. John: Extra Virgin
Most of the places listed above require a reservation. There are also several different dining options at the Ritz hotel (Alloro, Bleuwater, Sails) as well as a restaurant at the Ritz residences (Coconut Grove).
The hotel has a great spa if you are interested in booking a spa treatment. Pool cabanas can also be rented by the day or half day through the spa website.