If you have more time, take a walk across the bridge and have a good aerial view of the habour.
You could sign up for the half day climb of the Sydney Harbour Bridge and get certified.
There is also the Rock where you could have some refreshment while doing your shopping.
You could also take the ferry to the zoo or to the other side of the nude beach and take a bus back. Just take note of the timetable for the ferry as the last boat is at 5pm.
Sydney is the last stop for my backpacking trip as I have to leave the best for the last. Unfortunately it was raining for 3 days (on and off) during my 5 days of stay. Despite the bad weather, I continued to walk to the Darling Habour, Maritime Museum, Chinatown and the famous Sydney Opera Theatre. I even took the ferry (I think it is less than A$5) and had a tour of the magnificent habour.
It was during the Chinese New Year season when I was in Sydney but I did not feel the festival mood. People still go to work and the shops were still open as usual. I could only see a small performance in Chinatown.
I passed by the Universities, the Daring Harbour, get a closer look at the Maritime Museum and reached the Domain.
