My second favorite place in Seoul is Bukhan Mountain. It is a great half day hike with an amazing view.
Bukhan mountain is a great place to visit while in Seoul and should be on the top of the list for anyone who enjoys hiking or rock climbing. It's extremely easy to get to from INSIDE. Simply get on bus 109 and ride it 45 minutes until it stops in a parking lot. From there start walking up hill following the signs for the peak.
The bus only cost 1200 won and you can use your t-money card. Entrance into the park is free and you should plan on about 2 hours hiking each way. Be sure to bring water and if you want a lot of people bring snacks to eat at the top. My personal favorite is kimbap.
The peak offers incredible views of Seoul and is defiantly a must see during your time in Korea.
And if you are lucky,,,
you can met a friendly Korean hippy who was singing while he hiked down the mountain!