If you're going a long way in Oz, you fly or (if you're really adventurous) you drive yourself. The problem is that we have a land mass the size of continental USA with roughly 8% the population, and we mostly huddle along the edges. The middle is extremely pretty, but hardly anyone lives there and the climate isn't the friendliest. If you're well-prepared and have a reliable vehicle, the self-drive is very worthwhile. If you're in any kind of a hurry, fly.
We have some trains, but nothing like the US rail network. Pretty much just the major cities and towns are linked, and you can spend days on a train if you're going a fair way.
As for things to see... well, Melbourne is worth seeing for culture, Sydney is good for partying, and Brisbane has nice weather. No point in Adelaide unless you're planning to stalk Ben Folds. I've heard Perth is great, but it's a FUCKING long way away. If you want to see the reef you have to go way up north - Cairns, Mackay, Townsville, somewhere like that. I can vouch for Cairns, as we had our honeymoon there and it's a really nice town.
As for the Outback, most people like to do Alice Springs and Uluru (Ayers Rock), though they are quite a long way apart, about four hours drive, I believe. You could also go right up north to Darwin and see Arnhem Land and the wetlands up there. Apparently very cool.
The Tourism Australia website will probably have some useful info for you.
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