Sydney is arranged around a harbour, which means the water is the fastest way across it and the ferries are both transport and sightseeing. Build the days around that and the city opens up.
Everything below is on an Opal card, which caps daily and weekly.
Day one: the harbour
Early. Walk from Circular Quay round to the Opera House and on into the Royal Botanic Garden, following the shoreline to Mrs Macquarie’s Chair. Half an hour, free, and the view back with the House and Bridge together is the one you came for.
Mid-morning. Back through the garden to the Art Gallery of NSW — free, two buildings, and the Yiribana Gallery of Aboriginal art is the best in the country.
Lunch. Circular Quay, or the MCA rooftop café, which is free to go up and has the best harbour view of any café in the city.
Afternoon. The Rocks — the lanes behind the markets rather than the markets — then across the Harbour Bridge on the free pedestrian walkway, or up the Pylon Lookout.
Late afternoon. Barangaroo Reserve for sunset. It faces west, which nowhere else in central Sydney does.
Day two: the coast
Early. Train to Bondi Junction, bus to Bondi. Swim between the flags — this matters, and the article on the beach explains why.
Mid-morning. The Bondi to Coogee coastal walk, six kilometres of cliff path past Tamarama, Bronte and Clovelly, with ocean pools at most of them. Two to three hours with swimming stops.
Lunch. Coogee, or back at Bronte.
Afternoon. Bus back and out to Centennial Park, or into Paddington for the terraces and galleries.
Evening. Surry Hills for dinner — the highest concentration of good restaurants in Australia, ten minutes from Central.
Day three: the ferry and the Inner West
Morning. The Manly ferry from Circular Quay. Take the classic ferry rather than the fast one; it costs the same and takes the scenic line past the Opera House and out to the heads.
At Manly: the ocean beach, and the short walk round to Shelly Beach for the best snorkelling near the city.
Lunch. Manly, then ferry back.
Afternoon. Newtown or Carriageworks — and if it is a Saturday, the Carriageworks farmers’ market in the morning instead, which is the best in Sydney.
Alternative afternoon. Cockatoo Island by ferry — a convict prison and shipyard on a World Heritage site in the middle of the harbour, free to land and walk.
What to book ahead
Very little. BridgeClimb and any Opera House performance need booking; restaurants in Surry Hills often need a week or more. Everything else is turn-up.
If you have a fourth day
The Blue Mountains by train — two hours to Katoomba on an Opal card, then the Giant Stairway or the National Pass at Wentworth Falls. It is the best day out of Sydney and it does not need a tour.
The sun
Not a footnote. Australian UV is among the highest in the world and unprotected skin burns in about fifteen minutes in summer. Hat, sunscreen, shirt, and shade between eleven and three.
The seasons change this
Everything above assumes reasonable weather. Sydney’s are inverted from the northern hemisphere:
December to February is summer — hot, humid, and the beach days are the point. It is also school holidays and peak prices, and the middle of the day is genuinely fierce.
March to May is autumn and arguably the best time to be here: warm water, mild air, fewer people.
June to August is winter — 8 to 18°C, dry, often brilliantly clear. Too cold for most visitors to swim, but the walks and the harbour are at their best and Vivid fills the evenings.
September to November is spring, with whales migrating past the heads from late September.
If it rains
Sydney rain arrives in short heavy bursts rather than drizzle. The free galleries — the Art Gallery, the MCA, the Australian Museum, the Chau Chak Wing — will absorb a day between them, and the ferries run regardless and are better in weather than most people expect.
Two days, if that is all you have
Drop day three. Do the harbour and the Botanic Garden on the first, Bondi and the coastal walk on the second, and take the Manly ferry in the evening instead of the afternoon.
Getting oriented
Sydney’s geography confuses people because the harbour cuts through the middle of it. The CBD sits on the southern shore; North Sydney is across the Bridge; the eastern suburbs and beaches run out towards Bondi; the Inner West runs south-west towards Newtown; and the sprawl continues 50 kilometres west to Parramatta and beyond.
Almost everything a visitor wants is within about eight kilometres of Circular Quay, and the ferry, train and light rail all radiate from there.