Sydney - The Rocks
Sydney was founded on 1788 by Admiral Aurther Philip at Sydney Cove. That makes it the oldest city in Australia. The area around Sydney Cove is called The Rocks. This is the oldest part of the city, and many of the old buildings have been preserved and converted into shops, galleries, restaurants and pubs.
Walking around The Rocks is like going back in time. It is quite a big area, which makes exploring it more fun. There are lots of hidden corners, and although the old buildings are very well preserved they feel very authentic and not like a theme park.
Some of the best restaurants in Sydney can be found here - I would recommend Neil Perry's "Rockpool" for modern Aussie haute cuisine, Peter Doyle @ the Quay for seafood, and Bel Mondo for Mediterranean style cooking. There are also lots of art galleries to explore - check out The Argyle Gallery, Ken Duncan Gallery and the Museum of Contemporary Art.