I get this question a lot: "I just moved to Japan and need to open a bank account. Which bank do you recommend?"
While many Japanese people would likely recommend one of the big Japanese banks (like Mizuho or Mitsubishi Tokyo UFJ); personally, I would recommend Shinsei Bank because they're the only Japanese bank that comes to mind that caters to foreigners. They speak English better than I do. They have an English website. They don't scratch their heads when they see your middle name nor ask about your non-existent inkan. In short, they put more effort into capturing the niche foreigner-living-in-Japan market. The bigger banks don't really do that because they don't need to--they're big and already have massive market share. They're too busy counting their money to concern themselves with English-speakers.