My wife and i spent over a year in Melbourne and I'm glad to see your including it. Many people just stick to the east coast, but Mel-bun is a fabulous city.
places to stay: there's the nunnery in Fitzroy. It's quite central and even though it's a hostel it has reasonably priced double rooms. book ahead though. there's a number of excellent pubs and restaurants in fitzroy and i recommend it as an area to stay in. very close to downtown too.
I agree with the 12 apostles - quite breathtaking, but there's no shrtage of that in the whole country. Other stops might include the Melbourne Cricket Ground. Be sure to catch a footy match if there's any on. Third best sport in the world after hockey and that thing the afghans play on horseback with the goat carcass.
Make sure you stop in Nimbin while you're up towards Byron Bay. Granny's is a good place to camp or stay, though i found it much easier getting to Nimbin then it was leaving :)
In Sydney I highly recommend checking out the Priscilla Drag Show at the Imperial. It's free and a whole lot of fun. Just stick close to your wife ;)
That's it for me. Best of luck and congratulations!