Ogygia

Ogygia is the island that Calypso inhabits.

Description
Ogygia is a phantom island that exists everywhere and nowhere. It was designed as the prison for the nymph and daughter of Atlas, Calypso. It is a very gorgeous place, where there are invisible servants, and a beautiful garden, made by Calypso herself. Some of the garden's plants include the moonlace. Time moves differently there.

When Percy is leaving he says that he could come back and visit sometime, but Calypso tells him that that "No man has ever found Ogygia twice."

The hero Odysseus was marooned on Calypso's island thousands of years ago. He was saved by a plea from Athena to Zeus who sent a message to Calypso by Hermes to release him after seven years.

The Battle of the Labyrinth
Hera sent Percy Jackson to Ogygia to help him heal after he caused Mt. St. Helens to erupt. He was there for two weeks, but didn't know it since time flows differently on Ogygia, and decided to leave after a conference with Hephaestus. When he left, he claimed that staying in Ogygia would always be his biggest what if.