Scooby-Doo! and the Samurai Sword
The gang were lead there after following the riddled clues (solved by Velma Dinkley) from the Destiny Scroll, the first step in finding 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 hostile tribe nearby. They were captured by that tribe as they left the temple.