Commonwealth Bank
Everyday Smart Access + debit card + GoalSaver (newcomer)
No Australian address needed to set up the account (ID check at a branch when you arrive). No monthly fee if you deposit $2,000/month, are under 30, or meet other conditions.
Valid passport, foreign Tax Identification Number (TIN) or Australian Tax File Number (TFN), and an in-branch ID check within 14 days of opening. To earn the bonus rate: deposit any amount and grow your balance each calendar month.
Can be applied for online up to 14 days before arrival or within 12 months after arriving, or in-branch as a tourist.