Seoraksan requires permits now, and they ask you apply 3-15 days in advance. I posted English translations on a thread under "climbing chat". Technically this applies to Ahgulbawi, too, and permits can be picked up at either ranger station.
Do you have trad gear? If you want trad-- Mureung Valley
!! It's not far from Sokcho, and has some stellar cracks, with only the occassional bolt. Heading south, there are some amazing climbs at Yuhaksan (between Waegwan and Daegu). . . heading further South towards Busan there's Bueongsae
for fun long sport. For more remote (read: long approach) but also fun and amazing climbs near Miryang (maybe Dong-il is free during the week?:-) Sirubong
If you're heading this way, I have Friday's off, and would be happy to show you Yongseo
Can you be more specific about what you want (sport, trad, single or multi-pitch, easy approach or secluded and beautiful)?. . .
How long are you 'round?