My personal favourite Australian artist Ken Done has his gallery in the middle of The Rocks, near Circular Quay. Its constantly updated with his new and old works and well worth a visit!
With heaps of curves, greenery and natural light, this library is super conducive to working and learning — plus there's a secret slippery slide for kids that goes through the middle of the building, just for fun
Super nice cafe that runs the whole way through a block in Surry Hills. Awesome food and super fun staff + they have really good coffee. It's big so you always get a place and it's a super chilled atmosphere.