To answer your question: Cruise Sydney Harbour, swim at Bondi and/or Cronulla, climb the harbour bridge (mortgage may be necessary to buy ticket), fly around the blue mountains (buzz the three sisters), have a picnic in the botanic gardens, and for dinner you can either eat at Harry's Cafe De Wheels at Wooloomooloo or lash out for seafood at Doyles Watsons Bay.
That should see one weekend anyway...
If you want to live past 3 minutes after landing
LOOK RIGHT BEFORE CROSSING THE ROAD!!! Just a friendly reminder that we do things different hereabouts.