With its neoclassical Greek frontage and modern rear end, this much-loved institution plays a prominent and gregarious role in Sydney society. Blockbuster international touring exhibitions arrive regularly and there's an outstanding permanent collection of Australian art, including a substantial Indigenous section. The gallery also plays host to lectures, concerts, screenings, celebrity talks and children's activities. A range of free guided tours is offered on different themes and in various languages; enquire at the desk or check the website.

While the permanent collection has a strong collection of 19th-century European and Australian art, the highlights are the contemporary Indigenous gallery in the basement, and the collection of 20th-century Australian art, with some standout canvases by the big names of the local painting scene. Look out for Albert Tucker's scary Apocalyptic Horse, Russell Drysdale's brilliant gold-town street Sofala and half a room full of Sidney Nolans, including one of his extraordinary Ned Kelly paintings. There's a good representation of female artists too, including several Margaret Olleys on rotation. Brett Whiteley is represented by the intoxicatingly blue harbour of The Balcony 2.

The unfailingly controversial Archibald Prize for Australian portraiture exhibits here annually, as do the Wynne Prize (landscape or figure sculpture), the Sulman Prize (subject or mural painting), and the Artexpress exhibition of the year’s best school-student art.

The cafe and restaurant are fine places to hang out, with outdoor seating and views over Woolloomooloo Bay.