I spent approx. 1 year in Tasmania and I wont say I know it. For sure I sow lot's of places, but if you just use public transportation a stay will be in some cases a challenge, but it gives you lot of freedom for hiking and enjoying some place as long as you like, without thinking of the expense a rented car produce.
The best time I had when I spent some times or weeks in the national parks and do some bush walking. Even the most busy tracks are beautiful and gives you the idea spent some time at a remote place on this earth. For sure if you leave this heavy enjoyed areas you will be just by yourself, surrounded by wonderful nature.
To have a visit of all the different historical sides gives a deep view to the history of this small Island. Don't miss them.