Have a great time.
We lived in Perth for about 8 years and returned to the US about 2 years ago. We miss Australia dearly and plan to return sometime (we actually became Australian citizens while we were there).
The best time to go as far as Sydney, Perth or any of the other "southern" cities is Feb - April (which are their summer months) if your looking for hot weather and beach time.
The farther North you go the longer the summer season. The Great Barrier Reef is fun if you scuba/snorkel - go to the outer reef.
Depending on where you end up deciding to go do a little reasearch in terms of Jelly Fish, rain, etc which may effect your timing a little - especially if you go far north.
Many beautiful spots to stay along the coast outside of the big cities - the best thing if you have the time is travel up and down the coast rather than staying in one particular area.
The west coast (Perth) is a lot more laid back, beaches less crowded, cheaper (it terms of capitol cities) but another 4-5 hours by plane from Sydney.
Sydney of course has the harbour, opera house, etc.
It all depends on what you want to do and how long you have.
My wife's parents flew to Sydney and rented a camper van and spent 3 months driving 3/4 the way around the country - had a great time.