Jeju is an island in the south of Korea and is the largest island. The island has natural World Heritage Site is really famous for its nature, especially are Cheonjeyeon and Cheonjiyeon waterfalls, Mount Halla, Hyeobje cave (largest cave in the World and one of the World Heritage Site) and also many small islands, which are surrounding Jeju.
On the Mount Halla you can go hiking for two or three hours and you have a good view over the island, or else you can go horse riding, kayaking, swimming, hunting or fishing. Jeju offers for everyone something. But when you are lesser interesting in sport and more in the culture stuff, Jeju offers a variety of museum and can educate you in different topics, also in the sex museum for the more open-minded people.
Jeju is also interesting, because you can see Korea from a more traditional side and you can escape for some days Seoul. The fly is not expansive and the weather is good when you are going there in the end of May.