The Mandarin Oriental was an early arrival to the Sanya beach boom, and their Sunset Bar is a fantastic place to have drinks in the evening. It has a huge open space with a stunning view of Dadong Bay; it really is the best place in town for sundowners. The cocktails are surprisingly good—try the mojito—though they hit the wallet pretty hard.
For non-drinkers, they advertise a full high tea in the afternoons. I just love those little cucumber sandwiches with the crusts cut off.