Round Island is a secret area located in the northwest section of the map way out in the middle of the ocean. It doesn’t actually appear on the normal in-game world map but you can see its exact location using the map provided below.
Round Island is the secret area where you obtain the 
Knights of the Round Materia. The Materia is hidden inside a Materia Cave in the center of the island.
You cannot reach it using the Highwind. Instead, you will need to first breed and raise a Gold Chocobo. Check out the Chocobo Raising and Breeding as well as the Materia Caves side quest sections below for more information:
Chocobo Racing and Breeding
How to race and breed Blue, Green, Black and Gold Chocobos to reach some of the most remote areas on the world map and obtain some of the best treasures in the game.
The Materia Caves
The secret Materia Caves that you can reach with the Blue, Green, Black and Gold Chocobos.
The map below shows the location of Round Island on the World Map:
