Geeveston is a small Huon Valley town south of Hobart, with a forestry past that still shows in its visitor centre, timber displays, and carved figures around the streets. It is not grand, but it has a clear identity: this is where the settled valley starts giving way to wet forest and the edge of Tasmania's southwest.
The town itself gives you the Platypus Walk, Heritage Park, and timber history. The bigger reason to keep going is nearby forest: Tahune Airwalk for an easy canopy-level day, or Hartz Mountains National Park for alpine lakes and a much wilder feel.
Geeveston is best as a slow day from Hobart or as a base for the far south. It clears the bar because the town and its nearby forests make one coherent trip, not just a petrol stop on the way to somewhere better.