Liz' apartment is nice and clean. Staying with her is definitely good value for the money. The area is really beautiful, nice an quiet inviting to long walks. It possible to walk to the opera house and the botanical garden from there - although it is a long walk.
There are several breakfast places near the bridge. Breakfast at Kirribilli Wharf is good and in a nice setting but expensive.
There is a train station 10 min walk from the apartment, one stop away is the Central with connection to the airport.