Go to adelaide if you really want to, don't let me shatter your dreams.
everyone I met that had gone through or lived in adelaide had nothing but bad things to say. I personally hated it. It seemed like it was always closed. It seemed like a ghost town. weird considering it's supposed to have over a million people. I met a guy who was a firefighter there for 10 years, he asked me "was anybody awake when you were there?" just before I went there I met another guy who grew up there said it was often referred to as the "hole" or the "pit" of australia.
check out the australia explorer pass that greyhound has
the toughest thing is getting to the center and out. If you want to take a bus there it's going to have to be from darwin or adelaide. I don't think there is a one that goes from sydney...I imagine that would take a couple of days and it would pass through melb or adelaide....probably both. There may be a bus between the center and brisbane but I can't imagine it's any cheaper than a round trip flight. I remember seeing cheap flights to alice springs from melb but there might've been all sorts of restrictions, I never looked into it. idunno
but look at greyhound.com.au they have tons of passes they probably have one specifically for the cities you want to see.