Wander Salamanca Place: Explore historic Salamanca Place, one of Tasmania's best known landmarks. Explore the galleries, theatres, craft shops and restaurants in the 1830s Georgian warehouses.
Climb Mount Wellington: Mount Wellington's wilderness experience is 1,270 metres above sea level but just 20 minutes from the city centre.
Stay in Hobart's oldest suburb: Stay in bed and breakfasts next to grand old mansions and simple fishermen's cottages in Battery Point, named after a battery of guns put on the point in 1818. Or walk in the footsteps of convicts, bushrangers, whalers, sailors, barmaids and prostitutes on a ghost tour.
Visit Richmond and Kettering: You can walk across Australia's oldest bridge and stand in the cell of its oldest jail in picturesque Richmond, a 30-minute drive north-east from Hobart.
Fill up on seafood and fine wine: Savour classic cool-climate wines at the cellar doors and wineries of the Coal River Valley, Derwent Valley and Huon Valley, all a short drive from Hobart.
Source: http://www.australia.com/explore/cities/hobart/hobart-surrounds.aspx