Australia's east coast is three trips that happen to share an airport

Sydney airport is twelve kilometres from the CBD. You are at the hotel by midday and out the door within the hour. Walk Circular Quay, stand in front of the Opera House forecourt — not inside it, not yet — then buy an Opal card and take the public ferry to Manly. The return crossing takes thirty minutes each way and gives you the full harbour panorama, the bridge, the sails, the heads, all for the price of a bus ticket. It is the cheapest great harbour cruise in the world. Dinner tonight in The Rocks, Sydney's oldest street, where the sandstone buildings are the backdrop and the menu will have barramundi. Sleep early.

The Opera House guided tour runs most mornings and takes you through the concert halls, the backstage corridors and up to the views the audience never sees — book it the night before because it sells out. The afternoon belongs to Bondi: the clifftop walk south to Bronte is four kilometres of coastal scrub, sea stacks and bathers, and the Bondi Icebergs pool at the southern end is the most photographed swimming pool in Australia (you do not have to swim in it). The day ends with a dinner cruise under the Harbour Bridge as the city lights come on, the Opera House sails lit white behind you. This is the evening worth spending on.

The driver heads west on the Great Western Highway — ninety minutes to Echo Point at Katoomba, where the Three Sisters sandstone formation stands above the Jamison Valley. The Scenic World railway drops near-vertically into the rainforest below; the cableway brings you back up with the valley spread out beneath your feet. Most tours stop here. The better ones pause at a wildlife park on the return journey, which is the moment to see a kangaroo that is not behind a fence and a koala that is asleep in an actual tree. Skip the souvenir shops in Leura and spend that time at the viewpoints instead. The mountains are their own souvenir.

The IndiGo-code-share or Qantas domestic leg is three hours. The air changes the moment the aircraft doors open at Cairns — warm, thick, tropical. The afternoon is deliberately light: the Esplanade Lagoon is a free, stinger-safe saltwater pool right on the waterfront where the whole town swims, and it is the correct place to spend the first tropical afternoon. The night markets run along the Esplanade from 17:00; dinner here, the mud crab if you eat seafood, the laksa if you do not. An early night before the reef.

The fast catamaran leaves the Cairns marina early and reaches the outer reef pontoon in ninety minutes. Out here the coral is healthiest — the inner reef gets the run-off; the outer does not. Snorkelling gear is included and needs no experience; the water is warm, clear to fifteen metres, and the fish are indifferent to you in the best way. A guided snorkel safari and a semi-submersible glass-bottom ride are both included. An introductory dive can be added on board with no licence needed; the crew certifies you for one dive only, which is the right amount. Lunch is served on the pontoon. You are back at the marina by five, the reef still visible when you close your eyes.

The Kuranda Scenic Railway leaves Cairns Central at 08:30 and climbs ninety-three kilometres of track that took five years and 1,500 workers to cut through the rainforest in the 1880s. The train passes through fifteen hand-cut tunnels and stops at Barron Falls — a thundering waterfall best seen after rain — before arriving in Kuranda village, where the markets and the butterfly sanctuary fill two hours comfortably. The return is by Skyrail, a gondola cableway that glides just above the rainforest canopy for 7.5 kilometres, with two mid-station stops where you walk boardwalks into the forest itself. This is Queensland engineering from two different centuries, and both impress.

Three hours south and the climate shifts from tropical to temperate — you will want a jacket by evening. Check in, then the afternoon is a walk through what Melbourne does better than anywhere: Hosier Lane for the street art (it repaints itself weekly), the Degraves Street espresso strip where the coffee queue tells you the standard, the Royal Arcade and Block Arcade for the Victorian ironwork, and Federation Square for the view down Flinders Street. Dinner: Chinatown on Little Bourke Street or Lygon Street in Carlton — the Italian quarter that opened in the 1950s and has never closed. Both are correct answers.

The road starts at Torquay, where the surf shops tell you the coast has arrived, and runs 243 kilometres west. The driver keeps you on the ocean side. Kennett River is the koala stop — wild koalas in the grey gum trees above the road, watching you back — and Apollo Bay is lunch. The Twelve Apostles are best in the late afternoon when the limestone stacks turn gold and the crowds are slightly thinner than midday. Loch Ard Gorge is ten minutes west of the Apostles and tells the story of the 1878 shipwreck; it is short, dramatic and almost everyone skips it. Do not skip it.

A slow morning, then out mid-afternoon. Phillip Island is ninety minutes from Melbourne on the South Gippsland Highway. The Nobbies boardwalk runs over a fur seal colony — hundreds of seals on the rocks, audible before visible. Wallabies appear in the scrub near the car park at dusk if you look. The main event starts precisely at sunset: little penguins — the world's smallest, thirty-three centimetres tall — come in from the sea and waddle up the beach in groups to their burrows, as they have done every evening without fail. No photography is allowed anywhere near the parade. You simply watch, in the dark, as they march past. It is one of those things that should be clichéd and somehow is not.

A free day, deliberately. We brief you on options the night before: the Queen Victoria Market for last shopping (open until 15:00 on weekdays), the MCG guided tour for the cricket-mad — you walk the outfield and see the dressing rooms — the free City Circle tram that loops the CBD, or a slow brunch and a bookshop in Fitzroy. Ten nights in, the correct Australian luxury is an unscheduled morning. Pick one thing and do it without a plan.

Transfer to Tullamarine — allow ninety minutes from the CBD in the morning. Australia's biosecurity is strict inbound but your bag going home is the customs officer's problem, not yours. The correct final purchase is macadamia nuts from duty-free: they travel, they do not crush, and nothing says Australia more accurately. You land in India having seen a harbour, a reef, a rainforest and an ocean road that genuinely belong to four different worlds.