What are the most worthwhile things to do in Sydney on a first visit?

The Opera House rewards more than a photograph. Jørn Utzon's design won an international competition in 1957 from 233 entries — he was 38 and little known — and the building that opened on October 20, 1973, with Queen Elizabeth II officiating, had consumed 14 years and A$102 million against an original estimate of A$7 million. Its shells carry 1,056,006 glazed ceramic tiles made in Sweden, in glossy white and matte cream, and UNESCO inscribed the building in 2007 — less than 35 years after it opened, strikingly young for the World Heritage List. It is a working house, staging more than 1,500 performances a year; the guided tour runs daily, and the Concert Hall emerged from a two-year renewal in 2022 with its acoustics rebuilt.

The Bridge is the second text. Opened on March 19, 1932, its steel arch spans 1,654 feet (504 m) and tops out 440 feet (134 m) above the water — still the tallest steel arch bridge in the world — held together by more than six million rivets. Since 1998, BridgeClimb has walked visitors up the arch itself in guided groups; the free alternative is the pedestrian walkway on the eastern side, and the south-east pylon holds a lookout and museum reached by 200 steps.

The harbor itself is the third experience, and it runs on public transport. The ferry from Circular Quay to Manly — thirty minutes on the big harbor ferries — is the city's cheapest harbor cruise, ending at a surf beach a short walk from the wharf. Taronga Zoo is twelve minutes by ferry in the other direction, its enclosures terraced down to the water. On land, The Rocks preserves the lanes where the colony began in 1788, and the Royal Botanic Garden, established in 1816 on the harbor's edge, wraps the walk from the Opera House around to Mrs Macquarie's Point — the city's classic postcard angle.

The coast completes the set. At Bondi, the Icebergs club has maintained winter swimming at the beach's southern end since 1929, in an ocean pool the surf breaks into; from the same headland the coastal walk runs 3.7 miles (6 km) to Coogee past Tamarama and Bronte, and in spring it doubles as the route of Sculpture by the Sea. The one excursion worth leaving the harbor for is the Blue Mountains — about two hours by train to Katoomba, for the Three Sisters and the escarpment, and Scenic World's railway, inclined at 52 degrees.

Late in the day the BridgeClimb groups appear on the arch as a line of grey-suited silhouettes moving slowly against the sky, while below them the Manly ferry pulls out of Circular Quay into water the color of hammered pewter and the Opera House holds the last of the sun on its cream tiles.

The Bridge's four famous pylons hold up nothing. The arch's load travels into bearings in the abutments at each end; the granite-faced pylons were added, as the engineers of the day admitted, for aesthetic balance and public reassurance — to make the revolutionary span look as solid as it was. You climb the south-east one for a museum and a view, not because the bridge needs it.

• Morning — The Opera House tour on its first departures, then the Botanic Garden walk to Mrs Macquarie's Point while the harbor light is still eastern and clean.
• Midday — A ferry in the middle of the day, when the harbor is at its bluest: Manly for the beach and the corso, or Taronga for the zoo above the water.
• Evening — Cross the Bridge on foot at dusk on the eastern walkway, city lighting up behind you, and descend into The Rocks for the pubs and lanes.

Both icons ration their best hours: Opera House tours sell out on weekends and performance nights change which halls the tour can enter, while BridgeClimb's twilight and dawn slots — the ones everyone wants — book out weeks ahead and cancel in electrical storms. The harbor ferries run a reduced timetable in rough weather, and the Manly run in a big swell is an experience in itself. Sculpture by the Sea crowds the Bondi to Coogee path to a shuffle for its three spring weeks; walk it early or choose another stretch of coast.

Book the BridgeClimb and the Opera House tour before you book anything else, put the ferry day on the clearest forecast, and read the food question in this group for where the harbor days end.