Obviously, the Harbour Bridge and Opera House are amazing - they aren't icons for nothing and the Danish Design exhibit in the foray is well worth a visit. It includes many quintessential danish design products and highlights the talent we enjoy from our Copenhagen cousins.
The Marco gallery on Oxford st Paddington is well worth a visit. It currently has a portrait exhibition on and shows the variety of talent out there. A highlight is the Brigitte Mcnab portrait of a woman with daisies.
Paddington market is also a great spot on a Saturday. Have breakfast at Crate and then wander around. The market is full of emerging talent and on trend bargains.
The bookstores on Oxford st are very good. Ampersand is a used bookstore and cafe and they do an exceptional breakfast there. The bookstore across the road from there is also very good with mostly new books but some second hand - take a look.
If you are off to Sydney, make sure to stop in at The Commons off Oxford st, a wonderful bar that you go downstairs to. Sit back, have a Pisco Sour and enjoy the people watching and the music.