The famous Green Sand Beach in Hawai’i is also called Papakolea or Pu’u Mahana Beach. As much as I know it really has few competitors in terms of purity and freshness of the olivine sand. However, it is definitely not correct to say that it is the only one. The absence of evidence is not the evidence of absence. There is no need to go very far from the Big Island. Diamond Head is a tuff cone in Oahu that constantly feeds the sand beach right next to it with fresh olivine. The sand there is not as bright, but it is definitely composed mostly of olivine and it is green.

http://picasaweb.google.com/107509377372007544953/Hawaii#5881089836017624546
Layered tuff exposure right next to the beach that is the source material of olivine.
Sand sample from Diamond Head Beach in Oahu. White grains are biogenic fragments (corals and forams). The sand is not as bright as are the sample from Papakolea but it is still clearly greenish. Width of view 11 mm.
Olivine sand collected near the southern tip of Hawaii. It is from a tiny cove on the coastal trail, not from the beach itself where the grains tend to be duller green. Width of view 10 mm.
It is interesting to take a look at the Pu’u Mahana and Diamond Head volcanoes. There are some striking similarities. They are both located right next to the beach. They both contain lots of olivine. They are both composed of easily erodable pyroclastic sediments. They are both high and steep which speeds up the erosion.
Pu'u Mahana on the left and Diamond Head on the right. Images taken from Wikimedia Commons: jonny-mt (Pu'u Mahana) and Brian Snelson (Diamond Head).
Why is this needed for the green sand beach to form? Because olivine is unstable mineral at the atmospheric conditions. The transport route needs to be short and erosion fast to ensure that most of the olivine makes it to the beach and there is a constant supply of fresh material.
All right, we have Diamond Head Beach in addition to Pu’u Mahana but it is still only two and both of them are Hawaiian beaches. It may come as a surprise to many but olivine is not rare in sand. I would even say that it is an essential component of sand in many oceanic islands or volcanically active regions. Canary Islands, Iceland, Galápagos Islands, and Cape Verde are just a few names where olivine is a common constituent of many beach sands.
Sand sample containing lots of olivine from Ivgaq, St. Lawrence Island, Alaska. Width of view 15 mm.
I especially love a sand sample from the St. Lawrence Island in the Bering Sea. The climate there is not quite comparable to the Caribbean. That is perhaps the most important reason why this island is not very popular among tourists. The local Yupik people are quite protective about their island as well but I am lucky to know two of them. They sent me a very nice sample from the northern coast of Sivuqaq (St. Lawrence Island in Central Siberian Yupik). This sand sample is not as green as are the samples from Hawai’i because it contains lots of lithic material but olivine definitely dominates among the single minerals and gives greenish hue to the sand.
