Been a few times. Got married in Sydney. You'll love it, the natives speak our lingo, and are very friendly. If at all possible, visit the usual spots; Sydney is a must. Bondi is overrated, go to Manly Beach instead. Adelaide is beautiful & if you like wine, the Barossa Valley is close. The wine tours are brilliant I think (can't remember a lot of mine
).
For the Barrier reef, Airlie Beach & Shute Harbour on the Whitsunday Island coast is my pick. Lots of people go to Uluru & Alice Springs but remember how far away from everywhere they are; Alice is a 31/2 hour flight from sSydney & Uluru is a 7 hour drive from Alice. It's a big country.
If you hire a car, most companies stipulate you can't drive between dusk & dawn; it's when the 'roos come out to lay on the road surface (it retains heat) and kangaroo strikes are devastating.
Buy Bill Bryson's book Down Under, and get out & enjoy it, cobber!