Did a little more exploring through Google Maps and then expanding through Wikipedia and discovered Atuona on Hiva-Oa.
Quite remote in the South Pacific Ocean are
The Marquesas and specifically the island where Paul Gauguin was buried, Hiva-Oa. A cultural center was recently built in his honor in
Atuona.
These are not coral reef islands but volcanic. They are are so remote that clouds don't often reach them and so water supplies are not dependable.
Once well-populated (estimates 100,000 inhabitants), Westerners introduced smallpox and decimated the population. Now the natives number in the thousands.
They were encountered by American ships and were once named "The Washington Islands" but ownership claims were tenuous at best and the French created aliances with tribal chiefs that made this part of French Polynesia.