https://goo.gl/maps/CASG1bakg7w
Korea has many hills, ridges, and mountain ranges. The most well-known among foreigners is Soerak Mountain. But still others, Jiri Moutain, Taebaek, Sobaek, are also famous.
You can hike for several days or one day but it depends on the trails. All of them are good to visit in any season; Seorak in autumn, Taebaek in winter (its ranges are so beautiful covered with snow), Jiri for sunrise, Halla and Seonginbong are for basin.
Try to hike in Korea, it is different! You can see how locals enjoy their holidays in the mountains.