The second-oldest museum in Australia, this is where you’ll learn about Tasmania’s Aboriginal heritage, its history since settlement and the island’s wildlife. There’s also a collection of Tasmanian colonial art. A spectacular redevelopment in 2013 opened up new public and exhibition spaces, making this an unmissable stop on any Hobart cultural tour. Admission is free, and there are free 40-minute guided tours Wednesdays through Saturdays.