Day 1–2: Hobart for Salamanca, kunanyi / Mount Wellington, and MONA. Day 3: Bruny Island or the Tasman Peninsula. Day 4–5: Freycinet for Wineglass Bay and a final night back in Hobart or on the east coast.
This is a highlights version, not a full-island loop. Swap Freycinet for Cradle Mountain if alpine scenery matters more than the east coast beaches.