South Korea is definitely a fun place to be. Few places better embody the 24/7 lifestyle. I lived there for a couple of years and had a blast.
However, I don't think South Korea is likely to be the "tip of the spear", at least not in the next 10-20 years. Despite South Korea's relative success in the market, its R&D is still considerably behind Japan. South Korea is trying to move from being a top-notch manufacturer to being a center for innovation, but honestly it's still not there.
Also, please consider that South Koreans work longer hours than any other country in the OECD. The best-educated Koreans generally prefer to stay overseas because working conditions are better elsewhere. A friend of mine did recruiting for one of the Korean chaebols in the United States. Across the board, the Korean graduate students were all saying that they'd only go to the company if they had no other option. This is not a good situation when the best-educated elements of your populace don't want to come home.
Honestly, South Korea is in a tough spot, being sandwiched in between Japan and China. It's fortunate that it has a strong democracy (I'd stay stronger than Japan because they've been able to move between parties ...) and a business-friendly environment. However, it's still a small country with no natural resources.
I would love to be completely wrong about South Korea. I would love it if South Korea succeeded beyond my wildest imagination. However, I think it unlikely.
More likely, South Korea will shift from being a satellite economy of the United States to being a satellite economy of China.
For all the talk of the shift to Asia, venture capital, research and development, etc are still disproportionately in the United States and Europe. You're right when you say that the growth is in Asia. This doesn't mean that only Asian firms can succeed. Rather, it is quite likely that U.S. firms will sell to Asia.
I agree that the shift will happen at some point, but with regards to education, you're better off getting educated in the U.S., learning an Asian language in the meanwhile and making contacts at your school, and then trying to move into Asia. Your U.S. MBA (assuming it's from a good school) will demand a considerable amount of respect overseas.
If you do want to go to Asia, definitely go to a school that has a large international population, particularly from Asia. Get to know these people. They are the elites in their countries. Also, learn an Asian language (Chinese, Korean, Japanese). If you don't speak the language, you'll always be an outsider to some degree. Korean companies in particular tend to be xenophobic. Look at the executive ranks of Korean companies. Everyone is Korean or a Korean-American who is bilingual.
Fields that are well-known in Business School (consulting, finance, accounting) are still needed in Asian countries. A lot of schools have recruiters from overseas come. Again though, if you want to work in those countries, you need to know the language. If you're consulting with a Korean company, you need to be able to work with the locals. (McKinsey, Boston, etc. have offices in Korea). Same with finance and accounting. Honestly, the one area where your language skills can be mediocre and you can get by is probably the technical areas (science, engineering) if you can stomach it.
Here's wishing you the best.