Sydney Opera House — see it three ways: free from the outside and the Botanic Garden's Mrs Macquarie's Chair, up close on the one-hour tour (about A$45 / $31), or best of all from the water on a ferry.
Sydney Harbour Bridge — the BridgeClimb to the top runs from about A$300 ($210) and is a bucket-list splurge. Walking the bridge footpath is free, and the Pylon Lookout costs about A$19 ($13) for nearly the same view.
Manly ferry — the 30-minute ride from Circular Quay to Manly Beach is the cheapest great harbour cruise anywhere, about A$8-9 ($6) with an Opal fare. You pass the Opera House and the harbour heads on a regular commuter boat.
Bondi to Coogee coastal walk — 6 km of clifftop path linking Sydney's most famous beaches. Free, takes 2–3 hours with swim stops. Go in the morning before the sun gets harsh; carry water and sunscreen — the Australian sun is stronger than it feels.
Taronga Zoo — koalas, kangaroos and platypuses with the skyline behind them, a 12-minute ferry from the quay. Entry about A$55 ($38); the Sky Safari cable car inside is included.
SEA LIFE Sydney Aquarium — the Darling Harbour aquarium with dugongs and a walk-through shark tunnel. From about A$46 ($32). Best saved as your rainy-day card.
The Rocks — Sydney's oldest quarter, in the bridge's shadow: convict-era lanes, pubs from the 1800s and a weekend market. Free to wander, and it fills the gap neatly between Opera House photos and your ferry.
Skip Madame Tussauds and the wax-museum strip at Darling Harbour if your time is limited — Sydney's outdoors is the show.