Wineglass Bay is about a 2 - 2.5 hour drive from Hobart. The Nut is about 5-6 hours away..about 500-600kms.
Platypus are hard to get, they tend to dive and hide when they hear people. But there are some at Mt Field National Park, (Russell Falls), it is just a matter of being in the right place at the right time, and getting shot.
There are also platypus in the streams on Mt Wellington, though I have not seen one there at all.
If you want a beach with rocky outcrops etc, for foreground interest, Taroona Beach is always a good option for sunrise
For sunsets around Hobart, you can go to the top of Mt Wellington, Lindisfarne (near the Tasman Bridge) or Bellerive (looking across at Hobart city), or you can go further afield.
From Lindisfarne
From Bellerive