This isn't Seoul but taking advantage of limited space there are Bouldering options for every level and a few leading and ceiling routes. The gym is an A-frame structure on stilts with a loft in the center (roof problems available) and longer routes on either side.
Mr. Kim is very animated and speaks no English. You can climb as you like or let him train you! A few students and one older patron speak English. Otherwise, the climbers are friendly and range from beginner to competitve, but not elite. It's open M-F 6-10ish.
North of downtown and south of Jeonbuk University; SE of the bus terminal and walking distance. From the landmark Kyobo Building you can see the giant HITE sign on top a building; head there. On the side of the Hite Building, with a huge mural of swimmers, is a freestanding yellow --the only way to describe it is
"structure"-- with a huge sign that says "Kim's Climbing School".