The second-oldest botanic gardens in Australia, laid out in 1818 along a gentle slope down to the Derwent. The cool climate gives the gardens an unusual collection: a serious conifer collection, including kauri pines and ancient huon pines from Tasmanian rainforests; a Tasmanian native plant collection featuring the Pencil Pine and the King's Lomatia (one of the world's rarest plants, cloned from a single specimen); and a heated Sub-Antarctic Plant House that reproduces the conditions of Macquarie Island, the only such display anywhere in the world.
Allow 90 minutes minimum. The Japanese Garden, the Conservatory, and the historic Arthur Wall (a north-facing heated wall for growing temperate fruit) are all worth seeking out. The on-site Succulent Restaurant and Botanical Shop are good. Free entry and a short walk from the city up through Queens Domain.