Sanya is known for its pearls. They are considered to be the highest quality in all of China, so this is not the place to go discount shopping: Pearls at GN Pearl, a reputable pearl shop, cost 500–15,000RMB.
If you are just looking for something cute for yourself, or a gift, there are tons of local shops, and women selling pearl jewelry on the beach. Theoretically, a real pearl makes pearl powder when scratched, though the color and surface aren't damaged. However, there are a hundred tricks and scams, so it is better to buy something because you like it, and not worry too much about the authenticity. A pearl necklace from these sorts of vendors should be around 20–50RMB; don't pay any more.