Agree with Barb. You need to decide how long you are going to be in Australia for, and where you would like to see. If you want to stick to one coast or do you want to see say both Sydney and Perth which will involve a long flight to move from one side of Australia to the other.
For a first timer who has a couple of weeks, then I would suggest Sydney or Melbourne. Both amazing cities with so much to see and do. If you have extra time, then you could go further north to the Gold Coast, up to the Daintree or head inland. over 5 years ago