Curacao is part of the ABC (Aruba, Bonaire and Curacao) islands off the coast of Venezuela which is in South America. It is not on a continent but part of the Netherlands Antilles, a group of islands. The setting beginning is Curacao but the island Aruba plays a part. Near the beginning of the book, we learn that German submarines attacked the neighboring island of Aruba which is the smallest of the three islands. Curacao is the largest of the Netherlands Antilles. It was visited by European explorers in 1499, settled by the Spanish in 1527 and captured by the Dutch in 1634.
Although the setting is World War II, you can find out more about Curacao today and see some of the places mentioned in The Cay: Punda, Otrabanda, Willemstad, Queen Emma Pontoon Bridge and St. Anna Bay. Click on the reference link. Wilhemstad is a World Heritage Site.