Customs House library just opposite Circular Quay is another good library. Surprisingly spacious, it covers three floors. Best of all is a separate quiet room. And people really are quiet there!
This is something old fogeys like myself really appreciate. In the past people used to be quiet right throughout a library. But now, it seems pretty much accepted that you can happily talk inside a library at the same volume you do outside.
So, it's great when you actually find a place where people are seriously quiet and you can concentrate without interruption.
Like so many old buildings in Sydney, it's stunning.
UPDATE: Took this video a few days ago. Give a sense of the building's position in relation to Circular Quay.