The remote Pacific island is a tropical island somewhere in or on the outskirts of Japan, virtually untouched by civilization.
Scooby-Doo! and the Samurai Sword
The gang were lead there after following the riddled clues (solved by Velma Dinkley) from the Destiny Scroll. It was the location of the Temple of 1000 Steps, which would lead them to the Sword of Doom. They wanted to get there to get the sword before the Ghost of the Black Samurai did (although this turned out to be a big mistake).
They arrived at the remote island using Miss Mirimoto's automatic hover plane, which was a good thing because navigation by eye would have been difficult in the dense fog that always surrounded the island. They climbed up to the temple and found on it the symbol of the Green Dragon, a good sign for their quest since the Dragon was the one that hid the Sword of Doom. Shaggy Rogers managed to light the large Japanese lantern by accident, and they were able to read a map to the location of the Sword of Doom.
They also discovered too late that the map said there was a savage tribe nearby. They were captured by that tribe as they left the temple. The men and dog in the group were nearly cooked as an offering to the Green Dragon, while Velma, Daphne Blake, and Miyumi were nearly married against their wills to the tribal chief. Fortunately they were all able to escape when Velma was able to summon the hover plane using her laptop, which the islanders took to be a dragon.
They flew to the other side of the island and managed to extract the Sword of Doom from its heavily booby-trapped hiding place, discovering in the process that the Ghost of the Black Samurai was actually Sojo in disguise.