Hi Teppo, Welcome to KOTR and to Korea (for when you get here).
There is plenty of climbing available in Seoul. Bouldering, gyms, walls, granite trad routes and sport too. Alas the indoor ice wall (summer here now so no real ice) is closed indefinitely
I think the company went bankrupt or something...
BUT there will be a fair few of us available to climb that week I think. I'll be getting back into Korea/ Seoul late 21st....so maybe about the 22-23rd, or the weekdays after. Climbing the great granite slabs and cracks at Insubong Peak in Northern Seoul is best done on weekdays - weekends are so so busy! Other areas though are fine on weekends. Getting about is quite easy too as the Seoul subway is very easy to use and pretty fast.
Keep posting here as your trip gets closer and I'm sure you'll be able to join us all for some climbing.