Hi there, in response to your first sentence, there's really no "majors" in MBA. When you come out of a b-school, you get an MBA (not an MBA in Finance, or MBA in management). Unless you're speaking of a Masters in Finance, which is completely different from a traditional MBA. Having said that, all business schools will give you the proper management/finance classes for you to hone your skills on (kind of like saying you can go to Harvard Medical School or University of Oregon Medical School [not picking on anyone...] and get the same medical education to become a doctor...one's just simply harder to get in).
Not knowing exactly where you want to work, I'm going to take a stab that you want to be in Asia since your long-term goal is to go back there (as you stated). Look into HKUST and Nanyang, both are great business schools in Asia that have a lot of pull in the market. If you're looking to get into the US market, I'd recommend you looking into Georgetown, Boston U, USC, UNC range.
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