If you're looking to book some guided tours in and around Hobart (including to other parts of Tasmania), you can walk over to the piers and there are at least two tour companies operating from there. They have boat tours and bus tours. If you're one to prefer those types of tours, this is the place to go. It's right on the waterfront.
Either by airplane from Melbourne/Sydney, or by ferry (take your car if you have one) to Devonport, and then car or coach down through the state.
The Spirit of Tasmania I & II ferries sail daily from Melbourne, and there will soon be a Spirit of Tasmania III sailing from Sydney!
A rental car would be the best idea - buses also run every 20 mins or so along the busier routes.
Its easy to forget that the next stop south of Hobart is Antartica. The kids pointed out the artic expiditionary ships in the port and they knew where they were from too, this one ,i am reliably informed, is french.