Taiwan’s outlying islands contribute to a rich and many-layered experience of the country. Gusty Penghu Archipelago is about maritime history, graceful temples, and fine old houses. It also promises stellar windsurfing and fresh seafood. Green Island draws with clear waters, lively reefs, and a rare seawater hot spring. Kinmen and Matsu, lying between Taiwan and China’s Fujian province, offer handsome villages and Cold War relics. Between April and September, Matsu’s waters turn luminous from glowing algae. Dramatic rocks, jungled mountains, and vibrant tribal culture characterize Lanyu (Orchid) Island, the gorgeous home of the seafaring Tao (Yami) tribe.