Torvehallerne, Copenhagen. Photo by Thomas Steen Sørensen

As soon as the sun eases over Copenhagen, swarms of cyclists flow through the city’s cycle-ways, stirring an ambience of orderly calm. Packs of commuters wait patiently at traffic lights, gazing up at windows set in the pattern of the national flag. Taxis roll by emblazoned with stickers proclaiming the city’s carbon-neutral commitment. Even the sleekest of buildings are tucked under a height limit so as not to spoil the skyline.

To an outsider wondering why Denmark ranks as the second happiest nation on earth for the fourth consecutive year, the Danes’ easygoing efficiency seems a perfect illustration. In this country, the ‘hygge’ factor (roughly translated as a state of cosiness and relaxation) is a prized social commodity.

That dynamic is easy to spot in one of Copenhagen’s most popular attractions: Freetown Christiania, a commune where the laws hang a little looser. Its population of artists, rastas and punks – along with every colourful character in-between – have their own kindergarten, bakery and democratic system, as well as a hashish market with signposted etiquette.

It’s also home of the Christiania Cargo Bike, an adult tricycle with a box big enough to carry children. To speed through the surrounding ramparts on a saddle – past the quiet cafés, the walls sprayed with multi-coloured murals and a lake flecked with self-build houses – is to appreciate a tranquillity alien to other cosmopolitan cities.

By the afternoon, Copenhagen’s canal-sides become a prime lounging spot, even in mid-week. The embankments grow thick with throngs of fair hair and clear complexions, the revelry rarely raising above a quiet chatter. Some gather by the ubiquitous hotdog stands (‘wiener-mobiles’ licensed to those without other means of employment) for pølsesnak, or ‘sausage talk’, the vernacular term for banter between bites. Others congregate outside cafés to indulge in another Danish speciality, smørrebrød: open-faced sandwiches neatly stacked with cold cuts and spreads, often in ornate combinations assembled with precision.

Epitomising that appetite for detail is the New Nordic Cuisine Movement, a 10-point food manifesto emphasising simplicity, tradition and climate. When the chefs behind NOMA held a symposium for food experts in Copenhagen in 2004, they cooked up a set of values to advance the region’s culinary identity.

It’s a quest continued today in a floating food-lab moored along the city’s harbour, where chefs can tinker with new ingredients and techniques in the name of cutting-edge cuisine. Despite the progressive palates, however, visiting Copenhagen can be challenging for vegetarians. Many restaurants do not offer meat-free alternatives and asking if they might rustle one up can be met with a look of bewilderment.

Every September, a 10-day festival called Copenhagen Cooking hosts a series of tasting events and markets in order to flaunt the standards of a city boasting 15 Michelin stars. At any other time of year, an equally good spot to tuck in is the Torvehallerne food hall on Israel Plads, a gastro-complex packed with fish stands, cheesemongers, chocolate-makers and a treasure trove of delicacies. It also houses a branch of The Coffee Collective, one of the best coffee roasters in Europe, where the wooden countertops and high-stools provide a perfect spot to people-watch with a pastry.

Dusk is best greeted with a wander through Tivoli Gardens, a 20-acre seasonal amusement park that first opened in 1843, as this is when the crowds thin, the queues disappear and the lake begins to glow with the reflection of 120,000 lanterns dotting the scenery. Overlooking the melange of arcades and far-flung architectural styles is a 260ft-tall carousel ride called the Star Flyer, which elevates towards a perfect panorama of Copenhagen only to rocket off at 70km per hour, reducing the sun to an orange blur in your peripheral vision.

There are 45 cafés, bars and restaurants scattered across the fairground – ranging from fast-food to the best bistros in town – but if its white-knuckle rides leave you surging with adrenaline, one place to taper it off is the meat-packing district of Vesterbro. Located a 15-minute walk away, this nightlife hub is famous for seeing the paths of revellers and butchers cross before dawn, one crowd trudging to work, the other slinking home to bed.

Swish bars dedicated to high-end cocktails have proliferated across Copenhagen in recent years, even spawning a drink named after the city (an infusion of Bols Genever with a flourish of cherry liqueur and lime juice). But most notable among them is The Union, a speakeasy-style joint behind a blank door with a golden bell, and Lidkoeb, a wood-panelled 18th-century building that was once a pharmaceutical lab.

Copenhagen is compact enough to tackle in a weekend, with plenty of highlights worth cramming into that timeframe, though the ideal way to soak up its charms is a matter of choice. A Copenhagen Card (€42 for 24 hours, €75 for 72 hours) grants admission to 75 attractions and covers all public transport (including the 14-minute Metro tip to the airport).

To experience its splintered landscape like a true local, however, you have to cycle. The terrain is flat, the distances are short and there are bike rental units everywhere. A hop-on, hop-off canal cruise will burble its way under bridges between Nyhavn, the gentrified sailors’ quarter, and the old fisherman’s village Gammel Strand, taking in a peek at the Little Mermaid statue, a popular attraction commemorating the work of writer Hans Christian Andersen.

But to get the most out of a city that excels in avant-garde design and architecture, you can always roam on foot. The philosopher Soren Kierkegaard associated his daily walks of the city with his state of well-being – an experience worth recreating if only to visit the picturesque Assistens Cemetery (where Kierkegaard and Andersen are both buried) in the Nørrebro district, an up-and-coming area known for its small designer shops, chic antiques and vibrant bars.

For attractions further afield, the Louisiana Museum of Modern Art, an architectural landmark with a strong contemporary collection, lies a 35km train-ride away up the Danish coastline. The Blue Planet, a seashell-shaped aquarium situated just beside the airport, is the largest of its kind in northern Europe. The idea is to captivate younger visitors with a balance of the informative and the impressive, offering live feedings, storytelling biologists and a ‘touch pool’ to interact with the crustaceans.

Its centrepiece is a 4.1 million-litre saltwater tank with a cinema-sized window and a walkthrough tunnel, placing theatrical emphasis on a lifelike slice of ocean where hammerhead sharks, stingrays and eels weave among hundreds of tiny tropical fish. But if navigating a water wonderland amid the bustle of spellbound children sounds too much, the aquarium’s cafeteria opens on a sandy alcove overlooking the Øresund, a body of water separating eastern Denmark from Sweden.

Out there, if you can tear your attention away from the white wind-turbines spinning hypnotically on the horizon, you’re likely to find yourself in an idyll of picnicking families and kids quietly tossing stones into the waterside, stirring that same ambience of orderly calm.