Hi Hannah
It depends on what you need from a bank. If its simply a transactional everyday account, then you could also set up a HSBC account in Australia. HSBC is mainly online (there are a few branches here and there) and the good thing is you don't have to pay ATM fees or monthly fees. With the other big banks (CBA, Westpac, ANZ, and NAB) you have to pay a fee if you use another bank's ATM other than the bank you bank with.
Hope this helps.
T