Hi Wendy, I like Kate's suggestions but also recommend http://www.pendolino.com.au/ which is in the middle of the city. The best pasta I've had there is The Spaghetti Chitarra and would go back again just for that dish. about 10 years ago
There's lots of ways to become a "famous Italian restaurant" in Sydney, not all of them to do with the quality of the food and service. For instance, Bill and Toni's (http://www.eatability.com.au/au/sydney/bill-and-toni/) has been around for centuries, is a really buzzy place, good, cheap food and absolutely nuts late into the night.
If you want "famous for fine romantic Italian dining" you can't go past Mezza Luna, with gracious, skilled service and a knockout view of the city at sunset from most of the tables. (http://www.eatability.com.au/au/sydney/mezzaluna-rristorante-italiano/)
Want to see famous Sydney people? Go to Machiavelli's, which has a menu straight out of a time-warp and so-so quality and service, but everyone powerful in Sydney can be found there at least once a month, doing deals with other powerful people. (http://www.eatability.com.au/au/sydney/machiavelli/)
If you're visiting from elsewhere and want a great tourism experience as well as very good Italian food, you can't go past Bel Mondo in the Rocks with a view of the Opera House (http://www.eatability.com.au/au/sydney/bel-mondo/).
Buon appetito! about 10 years ago