Depends on what you want to see!
Far north Queensland (beaches, rainforest, great barrier reef) and the Northern teritory are beautiful(Kakadu, Uluru plus lots of other cool stuff) .
Sydney (harbour bridge, opera house, taronga zoo, hyde park) and Melbourne are great cities.
There's also some beautiful wine regions - Hunter Valley NSW, Yarra Valley Victoria, Barossa Valley South Australia and Margaret River Western Australia almost 9 years ago
I'm so tempted to say All of Australia :)
First step is to decide if you're here to see Iconic places like the Harbour Bridge etc, or want to experience the outback/rainforests etc.
The next step is to consider the time of year you are visiting. For example the top end QLD/NT are prone to monsoonal rains and cyclones at certain times of the year, then you'll have other issues such as snow or bush fire dangers in some regions at certain times of the year.
There is so much choice in Australia, it really comes down to your personal goals while you are here and the time of year you visit.
You can't go wrong with the major icons such as Uluru, Great Barrier Reef, Kakadu, The Kimberley's, Sydney, Adelaide and Melbourne are my favourite cities..... almost 9 years ago