Caldey Abbey is the home of Cistercian Monks and is one of Britians holy islands. The monks farm this small island that is just of the coast of Tenby. Caldey Island was /is famours for perfum and chocalate of all things. There are frequent boat trips from Tenby harbour out to the island. On the Island there is the medieval priory, museum, gift shop and tea rooms. There is also a very nice sandy beach, bu you don;t need to go on a boat trip to fine a nice beach in Pembrokeshire.
Further information here.