In no particular order:
http://www.australiancyclist.com.au/article.aspx?aeid=22236A great place to start is with our web site, at www.biketas.org.au and in particular here . The GIRO ride is around Tasmania, or the GIRO II is a shorter 2-week version. These are quite typical routes around Tasmania that people follow. In general the Tasmanian east coast is warm and dry (about 500mm or less annual average rainfall), and our west coast is wetter (up to 3000mm at the wettest point annual average rainfall). Both have hills. The west coast has temperate rain forest, is less populated and has a wilder coast line. Our predominant wind is from the west. Our capital city Hobart is actually the second driest capital city within Australia, so there's a fact you can impress people with!
For me the must-see would include the east coast and Freycinet Peninsula (pronounced the French way, "Fray cen ay"), the north-east from Weldborough Pass to Scottsdale and Lilydale, the north from Deloraine to Mole Creek, Sheffield and through to Cradle Mountain National Park (hilly), then the west coast from Tullah, Zeehan (great mining museum), Strahan, Queenstown and the Lyell Highway through the edge of the south-west wilderness area.