Australia spans seven climate zones, so the best month depends on where you're going. The southern states (Sydney, Melbourne, Tasmania) follow a four-season pattern: hot summers, cool winters. The tropical north (Cairns, Darwin, Broome) has only two seasons - the wet (Nov-Apr) and the dry (May-Oct).
By region: Great Barrier Reef and Top End are best Jun-Oct. Outback and Uluru are most comfortable Apr-Sep. Sydney, Melbourne and the Great Ocean Road shine Sep-Nov and Mar-May. Tasmania is best Dec-Mar.
By interest: Whale watching peaks Jun-Nov along the east coast. Wildflowers bloom in Western Australia Aug-Oct. Snow season in the Victorian and NSW Alps runs Jun-Sep.