The only white sand beach is at Sugar Beach, they imported the sand for the beach there form another island, it is very expensive however. Coconut Bay is near the airport but on the Atlantic side so the water can be rough but there is a section protected by a breakwall, it will still require a taxi or bus and about an hour ride to get to Soufriere. The Hummingbird Hotel and Still Beach House are on a nice small in Soufriere with snorkeling right from shore, they recently opened a tourist center with shops, restaurants, bars and chairs for rent at the beach. The Downtown Hotel is in the middle of town just a short walk from the beach, but not many amenities.
Most of the other hotels are up in the hills surrounding the town and would require a car or taxi to make regular visits to the many restaurants in town. Take a look at La Haute, I believe they offer a shuttle to Soufriere and Anse Chasenet (sp.) during the day.
Royalton is in the north and not really near anything and the buses don't go up that far. There are plenty of hotels in the Rodney Bay area Coco Palm is one of our favorites with many restaurants and bars within a 10 minute walk, however it's almost $200 round trip to get to the nature attractions in the Soufriere area by taxi.