Welcome to the site miniD!
In my experience I have enjoyed the sport climbing in jeollabuk-do
Soksal Bawi boasts, i would guess, at least 100 moderate to hard sport routes. if you like overhanging, limestone climbs this is the place. Busan has some great climbs in the city, though i don't know what the city is like in the summer concerning smog.
The nicest air and arguably the best scenary is up in the northeast, in Gangwon-do
. as you can see there is some sport climbing up that way. i have been to ganhyeon. it's not to big, but a lot of fun!
Given the things you don't like, i would suggest staying away from Daegu, Seoul and any city that does not have a major park butted up against it.
Daejeon is pretty nice given that is has a major national park bordering one side of the city. it's hot no matter where you go in the summer, but the smog isnt too bad in daejeon. also, you are within 2 hours of seonunsan which has soksal bawi, munbawi and the nearby halmae bawi. you can read about all these places on the site.
I know my info is a bit scattered. if you are considering a job, let us know what city it is in and then we may be able to give you some more info.
hope to see you out there in March!