If you have plenty of experience, try applying to the universities and colleges. They usually have the best deals for climbers lifestyles. You usually need a few years teaching experience, a TESOL/TEFOL cert and a Masters (in anything) really helps too, but a Bachelors in a "realted" field is often enough with some experience. I guess Seoul is the best place in some ways, but Busan is also a great city for climbers and a lot cleaner and less frantic. In fact any major city is usually pretty good (Daegu, Gwangju, Incheon, Jeonju etc). Try looking at Daves ESL cafe, or Top Gun Recruiting Korea (though that is mostly for Daejeon area jobs), or look in Seoul Global Centre. http://global.seoul.go.kr/global/vie...ng/working.jsp
That might get you started. It's not the best time to be looking now, a little late for uni jobs, as most have finished hiring by mid-Jan...but they often take on new staff around June also, and accept resumes and applications year round. Good luck, and be patient in trying to find a decent job. Salaries in the 2,000,000won-2,500,000won/ month are typical but all depends on the exact details of what your job expects etc. Accom is usually provided but small by western standards and usually only furnished with a gas-range, fridge, desk, chair, bed and wardrobe. Everything else you nee buy (second hand stuff is super cheap here).
Gear is expensive comp'd to States/ Europe so bring all your climb and camp gear.