I wouldn't come close to qualifying for the Raging Bull team based on my PRs but I am a Runner who has lived in various Asian cities for the last 8 years.
Japan = a fascinating culture with all the benefits of a 1st world economy. Extremely CLEAN (you won't realize what a dirty slob American you are until you go there, trust me). You are a 2nd class citizen. As Jason pointed out, very easy to score chicks. Awesome support for running, lots of first-class racing opportunities. Safe.
Korea = fascinating in a different way, easier to make a buck. Women are better looking than in Japan. Far less support/appreciation than Japan for running/biking/etc. You will not be a 2nd class citizen, but will never be Korean. Pray that the North doesn't invade again.
China = intriguing culture, massive opportunities. 8%+ economic growth for 25 years in a row. YOU CAN WORK ONLY 10 HOURS PER WEEK TEACHNG IN JUST ABOUT ANY CITY with free 1 br apartment, tv, etc., and truly live like a spoiled expat king: dining outside everyday (wonderful variety of cuisine, esp. for health-conscious or vegetarians), appearing on local TV shows (I've done it 4 times), juggling multiple cell phones packed with the phone #s of "modern" girls out for a good time with the local Big Nose stud, etc. Like Korea, there is little understanding/appreciation of running/cycling, but people will tolerate you. Many, many gorgeous places to train: best choice = Hainan, 2nd = Chengdu, 3rd = Kunming/LiJiang, 4th = Guizhou (huge friggin' province full of mountains), etc., etc.
Based on the above, I don't know why anyone (without a specific interest in Japanese or Korean culture, if so, great!) would choose Japan or Korea over China as a place to be a part-time teacher / full-time runner. You work less. You have more buying power. If you are somewhat twisted like Jason (take that as a positive or a negative based on your own inclination and personal family value brainwashing), you have more opportunities, too. And this is a HUGE country (larger than continental US) with many gorgeous places to run. If you don't believe me, go do some internet searches for pics from Sanya, Hainan or Lijiang for example.
Good luck Raging Bull, sub 2:20 is already awesome in my book. Prior to something like 1950 (I'm showing my ignorance here) you would be the Fastest Marathon Runner in the History of Time. But obsession can help give life meaning... isn't there a Japanese phrase for that?