There a few artificial climbing walls and a couple of crags near and around Seoul. If you like to hike there is the small crag in Gwanak (6-10 meters), Dobong (Never tried it but it's supposed to be 2 pitches), Bukhan (2-3 pitches). Being an amateur at this the highest I've ever been up is on an artifical wall in Ilsan (18 meters-ish) and there is a really nice artificial wall that's right next to the Han river at Ttucksome.
I climb with some friends everynow and than so give a call if you are interested, I'll see if we can arrange a bit of climbing and sightseeing.
+82 (0)10 4282 2012