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!
Underground food court in China Town with cheap eats and a mirror ceiling! It's in no way fancy, but incredibly charming. With about 12 different restaurants and a bar, its one of the best places in China town to get a meal.
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.
Japanese bookshop in the centre of of town. Amazing selection of art books, including a nice selection of independent publications. Lots of fun Japanese magazines, book and stationary. Excellent coffee shop inside too :)