Half of Tasmania is true wilderness and you want to avoid it (no roads so you won't have much choice; but even very experienced hikers routinely get lost there; I still remember the Australian army survival instructor who was lost for 2 weeks, never more than 5 km from civilization -- it can be that rough). The other half is beautiful and pristine farmland with easy roads. You could pick a place, like Pump House Point, and visit there
Lake St Clair Accommodation - Tasmanian Wilderness Retreat - Pumphouse Point ... otherwise it is all great. Bruny island is another idea but less easy to reach.