I will second the recommendation for the Lord Nelson Brewery. It was one of my first stops on my trip to Sydney this past summer. Great atmosphere, tasty beer and good food.
If you are interested in architecture, I really enjoyed the tour of the Opera House. I went back and forth on whether I wanted to pony up the cash for it, but am thoroughly glad that I did. Gave me a new perspective on the building and we had the good fortune of having a really charismatic and fun guide.
After walking around the Opera House working up a thirst, you can swing by the Opera Bar and quench it while soaking up views of the Opera House on one side and the Harbour Bridge on the other.