Disney's Castaway Cay island in The Bahamas in the Caribbean. Castaway Cay is a private island or "out island" in the Bahamas. Serving as an exclusive port of call for the Disney Cruise Line ships Disney Wonder and Disney Magic, the island is a popular tourist destination for families and Disney cruise ship travelers. The island, formerly called Gorda Cay, is located near Great Abaco Island. Today the island is fully owned by The Walt Disney Company, giving them substantial control over the experience of visitors to the island. A post office on the island has special Bahamian postage specific to Disney Cruise Line, and a "Castaway Cay" postmark.