Melbourne will be wet and grey but not cold by your standards (lows of maybe 5C). Since you have the pick of the country, I wouldn't go there in August. It's pretty nice around October/November though, especially if you like cosmopolitan cities.

You could do the ski areas between Vic and NSW but they're seriously crap compared to Whistler etc. I'm from Adelaide and I wouldn't bother being here in August - it's the coldest, wettest month, without even being spectacularly so. Kangaroo Island is good but there's a very good chance it will rain constantly in winter.

Do the tropical thing, whether it's east or west doesn't really matter. West is much more remote and with more-lumpy ground, east has more support for scubadiving, reefs, etc.