We booked a 2 bed apartment with Pacrim Apartments (www.pacrimapartments.com.au) for 4 weeks when we arrived, and were pleasantly surprised to be upgraded to a 3 bed townhouse which was fantastic with three kids (it's the Arthur St. townhouse on their website). It's a great place to start from, nice and close to North Sydney station on the North Shore line so easy to get into the city and good for househunting if you want to be North Shore - you don't have to navitage/pay the toll on the Harbour Bridge all the time).
The other option would be to book something through Stayz.com which is geared towards holiday makers but is quite reasonably priced (for Sydney).
second Kirribilli apartments. Really good spot at the end of the harbour bridge on the south side. Handy for the boat to Circular Quay or the train into town My folks stayed there when I got married in Sydney and loved it.