This is how easy it was to call Bank of America (non 800 number!):
http://gethuman.com/phone-number/Bank-of-America/
(Useful site)
The rep was surprisingly helpful and knowledgeable for my situation: they said they can easily open an account for me as a non resident I just have to show up at their branch. That's it. I'm still looking for a better option as per the topic title. The 3% forex fee on the debit card does not sound good.