Australian company and LLC in Michigan
Technically, you should have no problem opening a bank account for your U.S. company in Australia. A bank might require you to present them with certified copy of Articles of Organization with Apostille, and possibly a Certificate of Good Standing, also with Apostille, but this is something you should ask them directly.
The real question is what exactly do you need the bank account for, and based on that you will be able to decide where to open it. I invite you to read our article dealing with non-U.S persons opening bank account in the U.S.