This building is the Sydney Conservatory of Music - a part of the University of Sydney. It is located in the Sydney Botanical Gardens.
The Mitchell Library - part of the State Library of New South Wales. This building is also near the Botanical Gardens.
The Customs House Library - part of the Sydney library network. On the gound floor is a model of the Sydney CBD, which gives you a bird's eye view of the city. At the roof top is the popular Cafe Sydney where you get a beautiful view of the harbour.
The Museum of Contemporary Art - overlooking Sydney Cove. At the back is The Rocks area.
Besides the historical buildings, Sydney also have some interesting examples of modern architecture.