In Sydney u definitely want to spend a morning across the 3 southern beaches (Bondi, Tamaramma and Coodgie). Also some nice hiking available. Maybe a day trip to the Blue Mountains.
In Mel, try and make it out to see the penguins and possibly also the Apostles and the Great Ocean Rd.
Another thing to think of is hitting up some wineries either near Sydney or Mel. If u have more time the Barossa region around Adelaide is great.