Similar situation.
I walked in off the street and opened an HSBC Offshore account in Singapore. Obviously you need to prove ID, in my case Passport and Driving Licence.
Multi curruncy accounts and you can transfer to any international bank over the internet, set up regular standing orders etc.
Account comes with a Debit Card and you can also apply for a Credit Card if required, but they will usually ask for it to be secured against a term deposit.
Must say, I have been very impressed with HSBC, great service!