Julie wrote:

Citibank is in Australia and I believe Bank of America is in Sydney

True - but I hope the OP isn't thinking that an account in a US Citibank
account will be the same as having one in Australia.

A bank worth considering, and I don't know how big they are in the US
nor how low they can get the barriers between countries, is HSBC - it
prides itself on having the best international banking system, but I
have never had enough money to put it to the test.