Kiamo Ko is a castle located in the Vinkus. It is owned by Fiyero's family. This article contains mild spoilers for both book and musical.
In Gregory Maguire's Wicked: The Life and Times of the Wicked Witch of the WestEdit
In the book version of Wicked, it is home to Fiyero's family: wife, kids, sisters-in-law, and later, a house maid/nanny. Elphaba arrives here on a caravan accompanied by a mysterious boy named Liir. She stays with the family there, until they are arrested and taken away by the Gale Force. During her stay there, she is known as the Wicked Witch of the West, as she begins to study magic from the Grimmerie almost obsessively.
In Wicked: A New MusicalEdit
In the musical, however, things are different: Fiyero does not have a wife or children, and Kiamo Ko is described as simply "[his] family's castle in the Vinkus," which is abandoned as they live in another castle elsewhere. He and Elphaba plan to go there to escape the Wizard's royal guards. Only she is able to go, and she takes shelter there, holding Dorothy hostage.
In both book and musical, Kiamo Ko is where Elphaba is murdered by Dorothy.