Exactly which parts of Aus you want to visit will dictate the best times/seasons based on Australian seasons!!!!
Generally east and west coasts south of the Brisbane/Perth longitudes are best in autumn as weather is still warm and pleasant with nice mornings and balmy evenings. Spring is OK, but mornings can be still cool.
Melbourne hm, I don't support Mexicans
(that's what we call 'em) gets wet, they are known for cold weather. The coastline to the west of the CBD - Great Ocean Road is magical and I am still to visit, though it is about 1,000km from where I live. GUess not a priority.
Tasmania is best in summer. But they say that four seasons can be had in one day so not all is certain. Also this is high season so it is dearer.
Tropical east coast is best in winter as that's when it doesn't get too sticky and hot. Still warmer than the hottest European summers - well sort of.
If you are more specific about times we can help from downunder.
