Whaletail Island

Whale Tail Island is an island situated off the southwestern coast of the Earth Kingdom, in the Southern Air Nomad archipelago. The island gets its name from its distinctive shape, which bears resemblance to a whale's tail on maps.

While little is known about the island or its inhabitants, Water Tribe sailing lore claims that whales can never be found anywhere near the island because it is actually the tail of the largest whale in the world. The white coloring of Whale Tail Island on the world map suggests it was initially Air Nomad territory.

History
When Aang and his friends were searching for Appa in Ba Sing Se, they were led to an old stable where Appa was clearly being held. Wanting the Avatar to leave the city, the Dai Li had secretly installed one of their agents as a janitor at the stable, who mentioned to Aang in an offhand way that the bison was taken to Whale Tail Island, which would take many weeks to reach from Ba Sing Se. Eventually, Aang saw through this ploy.

It was revealed that this island was where the Southern Raiders had been stationed for some time, allowing them easy access to the South Pole for the annual purging of the Southern Water Tribe's waterbenders. Zuko and Katara, disguised in black ninja-like outfits, raided the flagship situated there. After interrogating the commander of the Southern Raiders, Katara discovered the location of Yon Rha, the man who killed her mother four years earlier in one of the raids.

Trivia

 * Though Aang hails from the Southern Air Temple, he did not know every island in the Southern Air Nomad territories, as shown when he asked where Whale Tail Island was.
 * It is possible that Whale Tail Island is not an actual location, but rather a play on words. The name of the island resembles the common phrase  That's a whale of a tale , or an incredible story (whales are large and incredible, while a tale is a story) that is not likely to be true. Coincidentally, every time something or someone has been claimed to be on the island, it has been proved that the person who said the  tale  was either mistaken or lying.