I agree on Doyle's, it's great

We'll be there the day after Christmas

My friend lives over in Watson's Bay, so it's near her house... Big thumbs up for Doyles...
We went to many restaurants over at Darling Harbour (that area has really grown) & Bondi.... just plan to spend plenty of time eating... lunch routinely lasted more than two hours.
I agree with what's been mentioned already, the Taronga Zoo, the Harbour bridge climb if you are so inclined, or just a cruise... Sydney is very much a walking city... if you won't be going out to the Bush, I'd recommend going to Featherdale Wildlife, it's close to the city.... Don't forget the blue mountains, but I don't recommend it if you are going in their summer... It really is quite hot once you get inland during their summer. Don't forget a tour of the Opera House.... We haven't hit Melbourne before, but we are this trip & the Great Ocean Road is planned for three of our days... see the twelve apostles while they are still up, just three or four months ago, the largest apostle fell.... it gave me a boost in the backside to put the GOR on our itinerary...
Are you going to Queensland? Cairns or Port Douglas (Cape Tribulation)? If you dive at all, that's where you'll want to go for some time as well.... If you don't want to go so far North, spend some time in the Brisbane area.. You can feed the wild dolphins that congregate nightly at Moreton Island, it's pretty amazing to be honest... then you can always visit Noosa, just north of Brisbane.... it was wonderful to see koala's for the first time in their natural habitat...
This time we are dedicating an additional 3 days for Kangaroo Island where the koala's will be plentiful & driving at night is not recommended (the animals all dart in front of you apparently)....
Oh, it just occurred to me, there is a Sydney City pass that includes most all of the tourist spots in the city... you pay for a certain number of days, Melbourne has the same thing as a matter of fact...