Australia isn't a cheap destination. When you get here you need time and money if you want to see very much at all.
I would suggest the following approach
1. Break the journey in Hawaii with at least a two night stay over.
2. Enter via Sydney or Cairns and spend a few days in either city getting acclimatised and seeing the sights.
3. Look for a holiday package that takes in Alice Springs, Uluru, Kakadu and Darwin if you want to see the Outback or one that takes you south to Canberra, Melbourne and Tasmania if you are more interested in history, culture and shopping.
If you have the time and the money after that try to go home via New Zealand. The scenery, particularly in the Sth Island, is absolutely stunning.