Hmm, it's going back a few years, but we stayed at the Harbor Rocks Hotel. (I know I am not a local, but places that are popular with tourists, while more expensive, sometime offer a better experience.) The Rocks area was nice with good food and drink, but while it is close to the night life, the bridge and the opera house, it is not close to the main shopping. We have a friend who at the time was overseeing the Paspaley Pearls store in Syndney, kind of like the Rodeo Drive area of the town. He took us around which was nice to have a local do, as we saw things we might never have otherwise done -- including some pretty pricey necklaces. He did take us to what may be a tourist dining establishment: Doyle's. It was down by the mouth of the bay and afforded a great view back to the city. The food was great, and the view amazing, but maybe pricey. Sydney is a pretty large city, so you may want to pick an area and explore, leaving other stuff for the next time. Auckland was only one night for us and unmemorable as the weather was poor. Good luck and safe travels.
Dave