I think - unless you have LOTS of funds - it is not a good idea to just pop into either South Korea or China (and, in China, it would be difficult for other reasons as well) and look for a job. Pre-arrange, but do your research. Talk to as many people as you can - it is the best idea to make contact with foreign teachers because their situation is the closest you will find to your own.

PS Once again, Michael has made a post without a single negative word in it. This is noted for those who think I can't and or won't do so.