I've just commented on one of your previous posts, sorry for the repetition, but which area will you be based in?
There are a number of sports that you can try out, depending on the area. Surfing (my personal recommendation!), scuba diving, rock-climbing, jet skiing and hiking are all options.
There are also companies that can take you para-gliding and canoeing.
It might be worth checking out this Expat Arrivals list of Australian expat blogs. There are a few posts about day-trips and exciting adventures, which are written for a 'non-Australian' audience.