One of these is Saba, a five square mile volcanic rock island. After a snack and, perhaps, a small tour, you can hike up through five levels of tropical rain forest to the island's peak. On a clear day you can get a great view of the entire Eastern Caribbean, with all of Saba spread out below you. When standing atop Saba, you will actually be standing on the highest elevation in the entire Kingdom of the Netherlands.
Another option is Sint Eustatius—known informally as "Statia"—where, on November 16, 1776, the American Brig-of-War "Andrew Doria" sailed into the harbor and fired its 13-gun salute indicating America's long sought independence. The 11-gun salute reply, roaring from the cannons at Fort Oranje under the command of Governor Johannes de Graaff, established Statia as the first foreign nation to officially recognize the newly formed United States of America while the revolutionary war was still in progress. In return, the British Navy sacked the island and it remains today, much as it was left back then.
Today, St. Eustatius has plenty of great options for outdoor activities. Its most popular hiking trails can be found at Quill National Park, where several trails ranging from 40 minutes to 4 hours go around and down into the Quill crater. Exotic flora and fauna of all kinds can be easily seen during your hike.