A place "under Down Under" as Tasmianians call their island has a (larger) bit of everything. I could perfectly imagine spending 3-4 weeks only in Tasmania. 1-1.5 weeks in the mountains (e.g on the Overland Track), then a few days in the Tamar Valley with lot of wineries, and finally a slow-paced tour around the both eastern and western coasts.
The island is of size of Bavaria, with only 500k population. The unpopulated space is occupied by mountains, forests, lakes, wombats, possums, etc. Therefore, the key words in Tasmania are "wilderness", "wild" and any derivation of these. Since i still did not sort my photos, this Wilderness Gallery may be of some interest for you.
Driving in Tasmania is a pleasure itself. Beautiful scenery, narrow, twisty, one-lane roads (still called highways). No-one but you. On the road you pass more dead animals than cars, which leads to a statistical conclusion that animal-hit count per driver is higher than 1. As statistics always lie, i didn't hit any.
Some other things the Tasmanians are proud of are wine, good mediterranean-like food (as one of the shopkeepers assured me they are on the latitude equivalent to Genoa) and Huon pine, which grows only in Tasmania and is a main material for any kind of souvenirs. Oh, and i almost forgot tasmanian devil, which is a nice little creature that you could easily adopt as a puppy, until the moment when it sees some raw meet and starts to fight for that with other devils. You wouldn't like to hear these growls at night.
BTW, how do they call the mainland Australia? "The North Island"