The gym in the basement of the Posco Building in Gangnam (Daechi-4 dong, Posco Center 02- 3457-0801
10:30 ~ 18:00) was the first place I climbed in Korea. It seems to still be there, as I found this link (with a map, albeit in Korean, but you can print and show a cabbie).
It used to be that it was only for building employees, though as a foreigner I was allowed to climb there. There were some folks there who spoke English and really gave me my start in the Korean climbing scene, when I was here only a few weeks and couldn't have told you the difference between a ㅁand a ㅍ!