Well , you can walk in just about any direction from there and get a decent breakfast BUT the weekend options are not as good as the week-day ones. Try the Bambini Trust cafe on Elizabeth Street. If you don't mind a walk then set off across the Botanical gardens to Wooloomooloo and then up the steps to Potts Point (20 mins and the steps are long and steep) - now you will be in real breakfast territory. Spring, Zinc, and Wedge cafes are all good - and all within a couple of minutes of each other. In the other direction from the hotel walk down to Circular Quay, once there you have a choice of cafes looking either at the bridge or the opera house - as it is winter now, looking at the opera house is a warmer and sunnier option.
