The Island of Jeju is dominated by South Korea’s tallest mountain, Hallasan, and I presume this offers the best walking on the Island. Nevertheless, there is a trail called Jeju Ole that circumnavigates the island, and is broken up into a series of sections. We (my wife Sophia and a few family members) walked a short portion of section 10, around the extinct volcano of Songaksan. It’s an easy walk and doesn’t require any hiking gear. The scenery was nice enough, including views along the coast in both directions, and to small islands which form the southernmost points in South Korea.
The village in the map below can be the start and end of your walk, although we started further down the coast and got picked up from this spot, where there’s a Starbucks and restaurants. I’ve rated the walk easy (it’s about 3km long), but perhaps it’s moderate if you start where we started. The track is obvious and constructed the whole way.