Atari's apartment will be my go-to Sydney place to stay and I have no reservations about recommending it to others.
It is located close enough to the city (or train) to walk to, but also serviced by a bus line (directly outside) which runs from Circular Quay to Bondi. The Darlinghurst area is well supplied with cafes and bars (and Atari provided lots of guides for these!), but quiet at night.
The apartment itself was warm and sunny during winter, with modern fixtures and all the expected amenities (even washing machine/dryer) and a kitchen. While we didn't need these facilities for a long weekend, this would be a terrific base of operations for a longer stay in Sydney.
Atari greeted us at the apartment at almost 9pm on a Friday night, after our flight had arrived, and showed us everything around the apartment, gave us a few local tips and pointed us in the direction of a bar on the next block over. Will definitely return!