My Australian bank is CUA. They charge a flat rate of $5 per overseas withdrawal which isn't great but beats the % charge by most banks. I don't really mind it because they have good exchange rates, better than the big Australian banks. Also, I only really use it for personal spending. Otherwise, I use Paypal for most online payments and also have a Payoneer account (which probably has worse fees).
The only Australian accounts I've seen that don't charge any fees are credit cards accounts which I don't want. If you are okay with that, ANZ has an account with no overseas transaction fees that they seem to be flogging a lot lately.