Beijing

Draped dreamily across mountains, the Great Wall of China is more gravity-defying beside the capital than anywhere along its epic course. Leave the city behind, and inside two hours you'll be watchtower-hopping along the undulating back of China's stone dragon. Restored stretches have cable cars to whisk you up to the battlements. For the rest – rambling, wild and remote – you'll need hiking shoes and a head for heights. Whatever your speed, a trip to the Wall is the ultimate bucket-list adventure.

For all its antiquity, less than a century has passed since the last emperor left the Forbidden City, the divine stronghold around which Beijing ripples outwards. It opened as a museum a year later in 1925, and such is its size that to this day previously unexplored halls, courtyards and cloisters continue to open to the public for the first time. Residing within are the ghosts of 24 emperors and their concubines, eunuchs, officials and servants; a humongous cache of treasure; and the essence of one of the world's great civilisations.

One of the great pleasures of Beijing is picking your way through the hutong, a dense matrix of residential alleyways shaped by the enclosing walls of traditional courtyard homes known as sìhéyuàn. Surviving in pockets, such as around the Bell Tower, the hutong are where you'll see local life unfold: gossiping grannies minding trussed-up infants; fruit-sellers, cleaver-sharpeners and rag-and-bone men (and women); and chess contests drawing enraptured crowds. A unique form of residential architecture found nowhere else in China, the hutong are Beijing's ever-diminishing heart and soul – visit before they're gone.

A divine conduit to the cosmos, here is where emperors were compelled by arcane ritual to drop a line to the big boss upstairs and beg their blessing. Peace and harmony reigned as long as fortune favoured the emperor. But god forbid floods, famine, earthquakes – signs that a ruler might be losing the mandate of heaven. Imbued with esoteric symbolism, the Temple of Heaven is a joy to behold, while the enclosing parkland reveals the locals at play, performing taichi, kung-fu or callisthenics under the gnarled old cypress trees.

Royal pleasure gardens of Empress Dowager Cixi, the Unesco-listed Summer Palace is a sprawling tapestry of hillside temples, pagodas, bridges and whimsical follies set around postcard-perfect Kunming Lake. Extravagant wonders like the 728m 'Long Corridor', adorned with thousands of individual paintings, the imperious Hall of Benevolence & Longevity, and the 'marble boat' pavillion draw the crowds, but the real tale here is a human one: of Cixi, the most remarkable woman in Chinese imperial history, ruling from behind the Dragon Throne in a man's world for nearly 50 years.

Beijing's signature dish gone global, proper Peking duck tastes better here than anywhere else. A perfect kǎoyā is a symphony of juicy lean meat and lacquered skin the colour of a St Tropez sunbather. Superstar chefs like Dadong go to molecular lengths in search of that elusive union of succulence and crackle. Compressed air, aged fruit wood, fans for drying... Nothing is wasted, either. The carcass is turned into a soup or crumbed and fried, while the webs, liver, neck and other bits can become delicious side dishes. Bon appetit!

Assess the state of the art at Asia's premier cluster of contemporary galleries, set within China's model 1950s factory complex. Big-name international superstars exhibit alongside the doyens of Chinese contemporary art, their installations on display in former factory workshops emblazoned with faded Mao slogans, where just a few decades back munitions and electronics were rolling off the productions lines for the new Communist regime. Hip cafes, edgy street art, and an elevated walkway offering views of steampunk-esque industrial architecture make the '718 Joint Factory', as 798 was originally known, a must-see.

One of central Beijing’s few hills, this sumptuous stump of green is the ideal vantage point to get your head around Beijing’s dizzying sprawl. Standing on a plaque that marks the city's historic central axis, you can see all the way north to the Olympic ‘Bird’s Nest’ stadium on a clear day. To the west, Beihai Park’s graceful white dagoba; to the east, the skyscrapers spear ever skywards; and to the south, the astonishing scale and symmetry of the Forbidden City, stretching far into the haze.

In a whirl of incense and creaking prayer wheels, Beijing's most atmospheric temple extends through a series of ever more divine halls to the marvellous finale, an 18m-high statue of Buddha carved from a single trunk of Tibetan sandalwood. Once you've reclaimed your jaw from the floor, there are side galleries crammed with Tibetan Buddhist relics to explore: ornate mandalas, icons of Buddha, tapestries, ceremonial robes, and no shortage of propaganda relating to China's historic claim over Tibet.

Catching sight of the Drum and Bell Towers for the very first time, looming authoritatively over grey hutong rooftops, is a genuine thrill. Once the tallest buildings in Beijing, these venerable bastions of time-keeping have sounded out the rhythm of the city for centuries. You can clamber up both for sweeping views of the Gulou (Drum Tower) neighbourhood, and hear a performance beat out on replica drums, before exploring the surrounding hutong – some of the liveliest and most enchanting in the city.

If these paving stones could talk. Mao's monochrome desert, site of the triumphant founding of the People's Republic of China in 1949, is better known outside the country for the tragic events that unfolded 40 years later. Decades of diligent censorship have just about scrubbed June 4th 1989 from the collective Chinese memory, but Tian'anmen Square still bristles with security, and tension reigns. Visitors descend daily at dawn for the patriotic flag-raising ceremony, before paying their respects to Mao, slumbering for eternity in his mausoleum on the square.

What Central Park is to New York, the lakes of Shichahai and Beihai are to Beijing. Flanked by drooping willows, Taoist temples, noble mansions – and in the case of Houhai and Qianhai, neon-girdled bars – they're the places for restful wandering by day and boozy fun by night. In the warmer months, pedal boats jostle for space, while in winter the ice throngs with trussed-up skaters, and you can count on a few hardy locals plunging through a break in the ice for their daily dip, to the delight of watching tourists.

Guarded by a dozen pairs of giant stone animals, mythical beasts and officials, this sombre funerary avenue leads the way to the grand imperial tombs of 13 Ming dynasty emperors, slumbering for eternity in a picturesque valley north of the city. En route, you'll pass the largest stone stele in China, mounted on the back of an enormous bixi (a kind of mythical tortoise dragon), before paying your respects at the three tombs opened for visitors, with grand halls and pavilions that rival the architecture of the Forbidden City.

Once a wildly popular art form, Peking opera still plays out most nights in theatres across the capital, from touristy taster shows to glittering gala performances at the National Centre for the Performing Arts. Peking opera rose to prominence in the 19th century and values beauty of movement above all else, so the uninitiated will be able to appreciate the artistry if not the language and coded symbolism. No such problems for the acrobatics shows, though, the best of them every bit the equal of Cirque du Soleil.

Roll up your sleeves and sift through the magpie’s nest of Chinese curios at this enormous covered market complex. Who knows? You might find Little Red Books, faded cigarette posters or even dusty photo albums of old Beijing residents among the wares of the 4000 or so vendors. Given that nearly all the antiques purporting to be from earlier dynasties are fakes, you’re extremely unlikely to snap up anything worthy of Antiques Roadshow, but you’ll certainly find a memento for your mantelpiece, and enjoy some good people-watching in the process.