If your going to be here for 3 days you won't be able to see uluru and the harbor bridge. I recommend going to Sydney, there is some snow about 4 hours from Canberra , i think.
I lived in an area that would be around four hours drive maximum radius from Ruapehu for nearly 40 years.
@OP, as much as you pissed me off with your wanker attitude and neg rep crap I have to say I am probably your best source of info on this particular topic.