This beautiful gallery, established in 1871, has a fine collection of international and Australian art that you should take time to see. Contemporary works are displayed in light-filled galleries with views of Sydney and the harbor, while colonial and 19th-century Australian art and European Old Masters are housed in the Grand Courts. There are also dedicated galleries for Asian and Aboriginal and Torres Strait Islander art. The gallery hosts more than 30 temporary exhibitions each year, including the annual Archibald Prize for portraiture (late March to early June), in which you’ll see plenty of famous Australian faces. Enter from the Domain parklands (across the road from the Royal Botanic Gardens) onto the third floor (ground level) of the museum. Allow at least 1 hour, probably more if you are interested in any of the many free tours on offer.