Climb Seongsan Ilchulbong (Sunrise Peak). This tuff cone rising from the sea is Jeju's icon. The stair climb takes 25-30 minutes and the crater-rim view is worth every step; sunrise is the classic time, but any clear morning is good. Entry is cheap — around ₩5,000 ($3).
Take the ferry to Udo island, 15 minutes from Seongsan port. Rent an electric bike or hop the loop bus for white-coral beaches and peanut ice cream — an easy, fun half-day.
See the Seogwipo waterfalls. Cheonjiyeon and Jeongbang (which drops straight into the sea) sit near Seogwipo town on the south coast, alongside the hexagonal lava columns of Jusangjeolli cliffs.
Walk in Hallasan National Park. The full summit hike is a serious day, but shorter trails like Yeongsil reward with volcanic ridges in half the time. In town-sized doses, the Manjanggul lava tube lets you walk inside a kilometre of cooled lava pipe.
Jeju also has Korea's quirkiest museum scene — teddy bears, optical illusions, chocolate — which is handy on a rainy afternoon with kids. Beach-wise, Hyeopjae (west) and Hamdeok (north-east) are the clear-water picks.