Melbourne

A narrow lane across from Federation Square where the walls, doors and bins are all under spray paint. A piece is painted over within weeks, so last year's photograph matches nothing. It carries on into Rutledge Lane behind, which is quieter.

Open since 1878, and in the deli hall shops European immigrants started are still trading. An old cemetery lies under the west car park: thousands of graves stayed and the market rose over them. A night market runs on Wednesdays for a few summer months.

A ground that holds a hundred thousand or so, and you walk to it from the centre. On 26 December the cricket Test begins here and runs five days. On days with no match a tour goes through the changing rooms and down onto the grass.

Returned soldiers cut this road by hand. Built as a memorial, the road is the headstone. Off Port Campbell limestone stacks stand where surf wore them away. Never twelve despite the name, and since one fell in 2005 the count slid from eight to seven.

Under the octagonal dome the desks radiate like spokes, and one lap of the upper gallery shows the whole pattern at once. You walk in without a ticket and sit anywhere, and Ned Kelly's armour is kept under the same roof.

Little penguins live in the gaps of the breakwater out at the pier's end. They return from the sea after dark, and volunteers stand along the rail asking people to put torches and flash away. Nobody takes a ticket; you watch from the rocks.

Eighty-two wooden bathing boxes stand in a single row on Dendy Street Beach, each painted differently. None has power or water, yet they are privately owned and change hands for what a house costs.

A narrow-gauge steam train that winds through the Dandenong Ranges, setting off from Belgrave. Sitting on the window sills with legs hanging outside is the old custom on this line, which is why every photograph looks the same.

The entrance is a wall of glass with water running down it, and many people put a hand through as they pass. The Great Hall ceiling is stained glass end to end, and the floor under it is left clear so you can lie down and look up.

Three floors of stone cells open onto a single well of a corridor. Ned Kelly was hanged here in 1880, and death masks of the condemned sit in the cells. A separate tour goes round at night by torchlight.

Opened in 1846, these free gardens roll over the slopes across the Yarra from the city centre. Wander between Fern Gully and the lakes and the traffic fades out. Climb Guilfoyle's Volcano, an old water basin reworked, for towers rising beyond the beds.

A stone memorial to the dead of the First World War, free to enter. It was built so that at 11am every 11 November sunlight through a roof opening falls on the word Love on the stone below. Mirrors and lamps now recreate that moment several times daily.

A museum of film, television and games inside Federation Square. Entry to its core exhibition is free, and a small card given at the door records whatever you tap so you can revisit it online. Many linger at the old consoles, which still play.

A domed hall raised in Carlton Gardens for the 1880 international exhibition, and World Heritage-listed in 2004. Australia's first federal Parliament opened inside it in 1901. It mostly hosts events, so seeing the interior means booking a tour.

An island about two hours' drive south-east, where after sunset groups of little penguins waddle out of the surf and up to their burrows. To protect their eyes, photography is banned. The sea wind bites in every season, summer included, so bring a jacket.

A native wildlife park where the Yarra Valley begins, upwards of sixty minutes north-east from the CBD by road. In front of a dim tank you can watch a platypus swim up close. Raptors in the flight show skim just above the crowd, and children duck.

An indoor arcade opened in 1892, its floor laid entirely with mosaic tiles under a glass roof. A tearoom trading since that same year stacks cakes in its window, stopping passers-by mid-stride. It links Collins and Elizabeth Streets.

The state museum beside the Royal Exhibition Building. Phar Lap, the racehorse that won the 1930 Melbourne Cup, preserved and mounted, draws the biggest crowd. At its core grows an indoor forest of living trees and birds, a calm break between galleries.

Open-air pools filled with mineral water drawn from deep underground at Fingal on the Mornington Peninsula. The pools climb a hillside, and the top one overlooks the peninsula's paddocks. Weekends sell out, so book days in advance.

A St Kilda foreshore fairground dating from 1912. Its wooden Scenic Railway, built that same year, is the world's oldest roller coaster still running. A brakeman rides standing mid-train, working the brake by hand.

An open-air museum recreating a whole 1850s goldfields town at Ballarat, roughly 90 minutes west by train from Southern Cross. People in period dress drive coaches and work the forge. Swirl a pan in the creek and tiny flecks of gold really do appear.

A yellow-brick railway station completed in 1910, the hub of the city's transport. Above the main entrance hangs a row of clocks, each showing the next departure on a line. It is the spot Melburnians mean when they say meet me under the clocks.

The Little Bourke Street quarter where Chinese miners settled during the 1850s gold rush, still thriving. Red gates guard both ends, with restaurants packed into the narrow lanes. The Chinese Museum keeps the long dragon carried in the Lunar New Year parade.