Dinky Island is a small island of uninhabited jungle—the only human character Guybrush meets on the island is Herman Toothrot. There are hints that there may have been earlier occupants: in the interior Guybrush is able to find such items as dynamite, a phone box, and a dinosaur and dolphin clipped out of a hedge. Guybrush must use nearly every item on the island to find the resting place of Big Whoop, and is led along the way by a parrot to whom he must give crackers for information.
Though the player is not given an overview of Dinky Island, some details about the geography are revealed elsewhere. When Guybrush finally finds all four pieces of the map to Big Whoop, he learns from Wally that Dinky Island is not too far from LeChuck's Fortress. Later Elaine, on Booty Island, is able to hear an explosion on Dinky. In later games multiple explanations are given for Dinky's location, causing some contradiction.
Dinky Island is a small island that Wally recognizes when he is able to put together the four map pieces he receives from Guybrush. It is only after he has been imprisoned in LeChuck's Fortress, however, that he is able to pass on this information, and he and Guybrush plan to go there in search of Big Whoop. Eventually they manage to accidentally destroy the fortress, and the explosion blows Guybrush all the way, coincidentally, to Dinky.
Guybrush finds Herman Toothrot on the island and navigates its small jungle to find a giant X, which he excavates with dynamite. He is stuck hanging from a rope until Elaine, who heard the explosion, comes to rescue him. After Guybrush explains his story to her (the events of the game to that point), the rope snaps and he falls into the dark.
In The Secret of Monkey Island, Monkey Island is a fabled destination that requires a voodoo spell to find. However, in Monkey Island 2, Dinky Island is a known and charted place, not too distant from islands such as Booty, and both Wally and Elaine are able to find it without any difficulty. This creates an inconsistency with later games in terms of Dinky's location. Herman Toothrot never reveals how he travels to the island.
In Curse, LeChuck explains to Guybrush the story of his search for Big Whoop, in which he manages to reach Dinky Island and the treasure just before Captain Marley and his crew. He says that Dinky Island is an atoll off the coast of Monkey Island--close enough to be connected by a series of underground tunnels (seen in Monkey Island 2)--and established Big Whoop as the "Carnival of the Damned" constructed on the island.
It is interesting to note that in official maps from Escape from Monkey Island, Dinky is identified as a small island off the north-west coast of Lucre Island (compare the Curse Tri-Island Area map to the one found in Escape [right]). Dinky Island being off the coast of Lucre (and thus closer to the Tri-Island Area proper) makes sense based on the in-game dialogue of Monkey Island 2. However, it just further confuses the issue regarding Dinky's location and connection to Monkey Island.