For people really new to Korea, the train is the best option as 6 trains a day go direct to Kanhyon
! They can walk from there to the climbing and a sport rack is perfect. Keep scrolling down from the link; I've listed the train #, departure and arrival times. Be away that these trains leave from Cheongnyangni, a smaller train station in Eastern Seoul, stop 125 on the dark blue subway line!
Bukhansan is mostly trad: slabs and cracks but it really takes some getting used to, can be epic, and a helmet is recommended (look at the placques to the dead). . . There is buldering near the campgrounds.
IF you wanted to venture further afield, you are welcome to come to Jeonju. . . I am likely climbing Sat at Maisan
, a very unique park (though a helmet is necessary for belaying here) and Sun either there are checking out a new crag by the local gym, the guys responsible for putting up many classic routes in Korea!
If I know when you'd come in, I could pick you up at the bus or train terminal. There are several trains and many many busses every day to jeonju, about 2.4 hours by bus and 3 by train from Seoul.