you can find "holiday" apartments for next to nothing per night. We went to Queensland. It'll be "winter" there but it's like late spring is Utah and very nice.
We did a little more time there (2 1/2 wks) but it was almost too much time for me because a lot of the novelty things took up a few days and were "been there, done that" for me. A week, timed right could be doable.
If you go to QLD, I recommend getting an apartment on the Gold Coast. Close to plenty of tourist things, great scenery, and close to an international airport (Brisbane).
BM me if you want some more info or suggestions...I can tell you where we stayed, etc.