Macquarie, ING and Up are 3 banks in Australia that don't charge international transaction fees.
The most straightforward way to avoid fees on each transaction is to bring cash with you. All you have to do is convert your Australian dollars to the foreign currency of the country or countries you plan to travel to.
You can convert your currency either online, and have your money delivered directly to you, or in-store.
Online money exchangers like S Money are often an easy and cheap way to buy foreign currency. You usually only pay a small fee and the currency exchange rate, no hidden fees!