Thought about driving?? we drove up the centre stopping at coober pedy,urldunda then accross to uluru,olgas,kings canyon etc back to urldunda up to Katherine and darwin stopping everywhere inbetween,depends how much time you have..camper van? or hire car...pick up Adelaide~drop off in Darwin stay in motels along the way?
Fantastic scenery so changable just make sure you don't arrive in the wrong places at the wrong time~rainy season!