Hi! I live in Brisbane but have lived in Sydney and the Whitsunday Islands (Great Barrier Reef) and spent a lot of time in Cairns.
There’s so much to recommend depending on how long you have here in Oz, your interests and age?
If you can buy yourself an Aussie Airpass, this will make flying from A to B a LOT cheaper. Alternatively, you can buy cheap flights point to point online with VirginBlue and Jetstar. Be sure to check the BAGGAGEALLOWANCES. If you don’t state what your baggage will be upfront, it can be pretty expensive to pay at the airport on check-in.
Ayer’s Rock & Alice Springs can be done combined, with a stop in King’s Canyon enroute. Accom. in all 3 places is expensive so you might want to opt for Backpacker or Motel style.
Cairns can be quite noisy, especially at night and if staying in Backpackers accom. If you’re in the 20’s age-group though, it might suit you and you’ll be sure to find lots of partying in Cairns. My advice would be to stay there only a couple of nights then make your way (easy coach transfer) to Port Douglas and do a Daintree Rainforest/Cape Tribulation Day tour from there. You can also do an Outer Reef cruise & snorkel on the reef from Port Douglas too.
Melbourne is an awesome city, as is Sydney. Both excel in food, art, culture, hip, quirk and funky. Sydney has Bondi Beach and the very groovy Newtown and cosmopolitan Melbourne has Brunswick St, St.Kilda and the amazing coastline – see the Fairy Penguins and the 12 Apostles.
**Great place to stay in Sydney is the Sydney Harbour YHA. It’s amazingly well-run, very affordable, clean & in a great location. It gets booked out quickly though so you must book ahead! Don’t forget to check out the amazing views from the roof-top deck if you’re there too!
Have a great time & a safe journey. I hope you enjoy Australia!