Do you like Asian cuisine? Billy Kwong's is run by Kylie Kwong who is one of my favourite chefs.
http://www.kyliekwong.org/BillyKwongs.aspx
For a more special occasion (with a price to match), you can see if there are tables free at
http://www.guillaumeatbennelong.com.au/home.html or
http://www.tetsuyas.com/index.html
Failing that (and I think they're booked up months in advance) we can try
http://www.ariarestaurant.com/defaul...ticle&ID=21609 or if it's a real Aussie Steak you want to experience, then Kingsley's is the place:
http://www.kingsleysauststeak.com.au
Half Day Monday, I would suggest popping around to our hotel in the morning, leave your bags there, then off to breakfast (Yum Cha in Sydney's famous Chinatown is right around the corner), and we can then tailor sightseeing for you until it's time to hop the train directly to the airport where we can wave lace handkerchieves at you and bid you a tearful farewell.