The standard advice on a first trip to Australia is to see both Melbourne and Sydney, and the standard advice is not quite right. The two cities are different in a way that most guidebook copy softens — Sydney is a harbour organised around a coastline, Melbourne is a European-inflected grid organised around cafes and trams — and a genuinely satisfying week in one is usually more rewarding than three rushed nights in each. That said, the flight into Australia is long enough that most travellers will want to see both, and the question becomes one of ratio and sequence.
Sydney sells itself in the first two hours after arrival. The harbour is genuinely one of the world's great urban settings, the walk from the Opera House around Farm Cove to the Botanic Gardens is one of the finest half-hours a city can offer, and the ferry system — every commuter route also a scenic cruise — is a public transport wonder. The east-facing beaches from Bondi south to Coogee are working beaches with cafes attached, and the six-kilometre coastal walk between them is the honest first Sydney morning.
For a base, Park Hyatt Sydney is the only hotel in the city with the Opera House on its doorstep, and the north-facing rooms on the upper floors with the Opera House view are the rooms to book. The premium over a harbour-view room without the Opera House is substantial and, on a first visit, worth it — the entire point of being in this hotel is the view from the room. Book breakfast on the terrace rather than in the dining room; the light on the Opera House sails at seven-thirty in the morning is what you came for.
Melbourne is slower to reveal itself and, for a certain kind of traveller, ultimately more rewarding. The city has a coffee culture that is not a marketing claim but a demonstrable everyday fact — the barista at Patricia in the CBD is the standard, not the exception — and the laneway system through the centre (Hardware Lane, Degraves Street, ACDC Lane) turns walking into a proper activity. The Queen Victoria Market on a Saturday morning, the National Gallery of Victoria's Ian Potter Centre in Federation Square, and the ferry across to Williamstown are three honest half-days.
The practical case for splitting a fortnight is roughly five nights in Sydney, four in Melbourne, and the remaining five in a third location — either the Great Barrier Reef out of Cairns, the Kangaroo Island wildlife circuit out of Adelaide, or, for a certain kind of traveller, four days in the Barossa Valley and one on either side in Adelaide. Trying to add Uluru, the Whitsundays, and Tasmania to a two-week trip is the mistake most first-time visitors make.
A counterpoint no one mentions: Tasmania. A three-night trip to Hobart with MONA and a drive down the Tasman Peninsula is not a substitute for either mainland city but complements them in a way that makes a fortnight feel considered rather than rushed. The direct flight from Sydney to Hobart is under two hours.
On timing, the shoulder seasons — March through May and September through November — are the honest windows. The summer months, particularly January, are hot enough in Sydney that the coastal walks become unpleasant by ten in the morning, and hot enough inland that any trip beyond the coast requires early starts. Winter in Melbourne (June through August) is genuinely cold and wet, and while the coffee culture only sharpens, the sightseeing suffers.
One practical detail: internal flights within Australia are more expensive than distance would suggest, and often need to be booked as separate tickets rather than through the international carrier. Budget for four to six hundred dollars per person on domestic legs across a fortnight, and book them at the same time as the international leg.