The state museum, occupying a cluster of Tasmania's oldest stone buildings on the waterfront — the 1808 Commissariat Store is the oldest building in Hobart. The collection is strongest on Tasmanian natural history (including a small but harrowing exhibit on the extinction of the Thylacine, the Tasmanian Tiger), colonial paintings by John Glover and W.C. Piguenit, and Tasmanian Aboriginal cultural objects. The shell-necklace display from the Bass Strait islands is a quiet highlight.
Allow two hours. The free admission and rambling layout reward unhurried wandering. The on-site Courtyard Café is one of the best lunch spots in the CBD.