Yay, that's great you chose Tassie!
Suggestions would be...
Richmond - There is a super fun maze for kids, a place called Zoodoo where they can see animals and watch shetland ponies race, an old jail which is said to be haunted, Australias oldest bridge, beautiful places to stay, a 'sweets and treats' store that the whole family will love, and lots of quaint little shops that sell items made from Tasmanian woods. It's 20 minutes from Hobart.
Launceston - I'm not so familiar with Launy but there are lots of great touristy places to go to there as well. Penny Royal world was a lot of fun when I was a child.
Port Arthur - Before the massacre it was a humbling experience to walk around the old jail and see how the prisoners lived. Since the massacre it is even more of a humbling experience. There is a beautiful memorial to those who died. You can also do a cruise or take a guided tour. They also put on a ghost tour in the evenings which is fun.