The impressive Surry Hills Library and Community Centre was designed by architects Francis-Jones Morehen Thorp and it's a stunning space. Filled with books, of course (there's a large collection of fashion and design titles), as well as sofas, chairs and tables by the front windows to work or read while sipping on a coffee and using the free wifi. Rooms upstairs are available to hire for functions/fitness classes, etc.
Recently rebuilt from ground up, and facilities are excellent. Get there early though if you expect to get computer access or a seat to relax in. Very busy most of the time.