Would you consider an apartment? We stayed at Kirribilli Apartments early June for 3 nights - A$130/night + one-time A$80 cleaning fee. It's an independant operation, hence no hotel/airline miles.
There is a small supermarket/deli, and excellent restaurants literally out the front door - and the local watering hole is a short stumble away!
Fantastic location => 3 minute walk to Sydney Harbour or Milson's Point train station (no more than 10 minutes into the downtown Sydney). Apartments have been recently renovated. I think my wife took some photos of the apt so PM if interested.
These Australian discount web sites give an idea of what is available. When bookings are made through these discount web sites Frequent Flyer miles and hotel loyalty points are usually not earned. Often booking direct with the hotel is the same price or lower than these discount web site's.
We've always stayed in serviced (self-catering) apartments. If you like the Darling Harbour area you could try Southern Cross on Harbour but it is getting a little worn around the edges, but the price is right (A$140 for 1BR, last I checked.) The Southern Cross Apartments (now Trendwest) have undergone some refurbishment and have improved, or so I hear, at the corner of Goulbourn at Wentworth, for about the same price.