The ROK Drop blog has an excellent post on getting into the wild in Korea:
Seoul is a city that is literally surrounded by mountains that provide many great outdoor opportunities for those who want to escape the hustle and bustle of modern, urbanized Korea.
The most popular destination for Seoulites looking to get away from the city and reconnect with nature for a little while is a day trip to Bukhansan (Pukhansan) National Park that towers over the northwestern landscape of Seoul.
So many people visit this park that it is actually the most popular national park in all of Korea. On some days its popularity with the locals leaves you wondering if you have actually left the city or not when you are surrounded with visor wearing ajummas and ajushis dressed as if they are about to undertake a Himalayan expedition.
To escape the crowds, you have to get away from the lower reaches of the park where visitors congregate around the restaurants and soju bars and find your own piece of solitude on one of the upper peaks of the park. …
This national park was first established in 1983 and encompasses nearly 80 squared kilometers of land. There are three main peaks on the mountain, Baekundae (836.5m), Insubong (810.5m) and Mangnyeongdae (799.5m).
This travelog will focus on the route up to the highest peak Baekundae. …
Bukhansan National Park – official website