Canberra

Entry costs nothing. Every day in the late afternoon, at 4:55pm just before closing, the Last Post Ceremony reads out the life of one fallen soldier and a bugler plays. Red poppies left by visitors fill the gaps beside the names cut into the cloister walls.

A parliament sunk into a hill with lawn laid over the top. Expect airport-style screening on the way in. On sitting days the 2pm Question Time fills the House of Representatives gallery quickly, so queue early.

A dammed stretch of the Molonglo River, with the Captain Cook Memorial Jet firing water skyward from the middle. The shore loop between Commonwealth and Kings Avenue bridges is roughly a seventy-minute walk. On windy days the jet is switched off.

In 1973 the government paid a huge sum for Jackson Pollock's Blue Poles and the whole country erupted; the painting now stands for this gallery. The permanent collection is free, and out in the sculpture garden one work releases fog at set times.

A loudly coloured building on the end of Acton Peninsula. It keeps the heart of Phar Lap, the 1930s racehorse, in a glass jar, while his hide is in Melbourne and his skeleton in New Zealand. There is no entry fee for the permanent galleries.

The hill behind the War Memorial. From the top Anzac Parade runs over the lake to Parliament House in one line, the city's founding axis. The footpath up from behind the memorial takes about forty minutes, and a road reaches the summit car park too.

Only native Australian plants grow on these slopes of Black Mountain. Misters keep the rainforest gully humid though the country around is dry and inland, and red desert sand covers the Red Centre Garden. Entry is free, though parking is charged.

Giant antenna dishes run with NASA rise where the Tidbinbilla valley opens out. This is the only ground station on Earth able to send commands to Voyager 2, and the visitor centre is free.

A protected valley southwest of the city, where eastern grey kangaroos sit on the verges as you drive the loop road. On the wetland trail platypus surface around dawn and dusk. A fee is charged per vehicle at the gate.

A market held only on Sundays inside the former bus garage at Kingston. Crafts, secondhand books and tastings of local wine pack the shed, and arriving at opening time makes parking easy.

The national science and technology centre on Lake Burley Griffin's edge, where you touch and operate most exhibits yourself. A near-vertical drop slide is the hit with children. Skip weekday mornings, when school groups pour in, and it is quiet.

A free gallery devoted to the faces of Australians. Explorers, athletes, singers and prime ministers hang together regardless of era, a quick course in who matters here. It stands next door to the National Gallery, so see both together.

The white building that housed Parliament from 1927 to 1988 is now the Museum of Australian Democracy. Old chambers and the prime minister's office survive intact, and you may sit in the seats. On the front lawn stands the Aboriginal Tent Embassy, since 1972.

After the 2003 bushfires burned a pine plantation off this hill, rare trees from around the world were planted forest by forest. A pavilion holds bonsai and penjing, and the summit overlooks lake and city. Families crowd the playground of giant acorn pods.

A mountain park covering almost half of the Australian Capital Territory, in its south. Get directions from the visitor centre, then follow the Yankee Hat track to Aboriginal paintings under a rock shelter. At dusk mobs of kangaroos graze the grassland.