About halfway between China and Japan, just off the SW tip of Korea, is Jeju-do. Dominated by lake-filled Halla-san volcano (extinct, and incidentally, the highest peak in South Korea), this subtropical island has been known for its horses since the Mongols brought them in the 1300's.
Green tea plantations are found on the southern slopes of the island, and fresh seafood, predictably, is plentiful. (If you're feeling especially brave, try fresh sea urchin; Japanese tourists love the stuff.) Vaguely Polynesian-looking stone 'grandfather' statues can be found everywhere, along with tangerine groves, palms, and lava-rock walls. You can hike one of the world's longest lava tubes.
Jeju-do is also known as the 'island of wind, women, and rocks.' Its culture and dialect are distinct from peninsular Korea. Some have called it 'Korea's Hawaii,' others liken it to Ireland...and my wife and I found the climate and vegetation on the southern coast reminiscent of Costa Rica...
Numerous flights connect Jeju-do with the South Korean mainland, as well as with Japan and China. A few posh beach resorts (with golf) exist, but the island is not quite completely 'polished' yet for international tourism...which adds to its charm. (And the island is very proud that is has multiple UNESCO world heritage sights.)