On our first morning, Copenhagen offered petrichor, pastries and perfect coffee as bicycles ticked past. Minutes later we had passed a palace and watched pedestrians await green lights despite empty roads. The streets looked as if litter required planning permission, though 14 of 40 fountains remained dry after two specialist staff resigned - an embarrassment measured in empty basins. Those basins were conspicuous precisely because almost everything around them worked.

Noma reopened a fortnight before we arrived under executive head chef Pablo Soto, with René Redzepi returning as creative director rather than daily operator after renewed scrutiny of the restaurant’s working culture. Yet Copenhagen no longer needs one restaurant - or one chef - to speak for it.

Koan was our first dinner. The dining room turns its back on the waterfront and towards the pass and sommelier station. Nearby, a block of Korean granite, given by Korean veterans, honours Jutlandia, Denmark’s hospital ship during the Korean War. Two stars were on the door; three-star cooking was on the table.

The restaurant began as a pop-up at Empirical Spirits in 2020, then opened permanently here in April 2023. Ten weeks later, Michelin awarded it two stars.

Born in Seoul and adopted by Danish parents, chef-patron Kristian Baumann trained at Noma, Manfreds and Relæ, and helped launch Noma Japan. When Redzepi took Noma to Australia, Baumann occupied its Copenhagen kitchen with 108; Michelin arrived six months later. A first research trip to South Korea in 2017, followed by regular returns, helped turn curiosity into a language. Koan cooks in the charged interval between birthplace and upbringing.

Service was balletic, though nobody asked us to admire the footwork. Jeff Njoroge Njehu guided us through 18 courses without making dinner sound like coursework. Hand-peeled raw shrimps, poached oyster and scallop led to acorn, white kimchi and silken tofu with caviar. The white-kimchi flower arrived in a ‘Reborn’ bowl by Korean artist Lee Ki-jo, made with fragments of Ming and Qing porcelain. Broken material returned in another form.

Chilled lobster noodles, kkwabaegi, summer salad and plump langoustine followed. The menu’s spare nouns withheld the plot until each dish arrived. Gamasot rice with forensically displayed accompaniments yielded to its caramelised base before a Korean-accented run of sweets.

Head sommelier Lasse Peder Nielsen’s pairing refused a single compass. Yunguna, an experimental Copenhagen rice winery, supplied takju - cloudy, unfiltered Korean rice wine - and yakju, its clear counterpart. Fourrier Gevrey-Chambertin Premier Cru Cherbaudes 2019 brought Burgundy into the middle. Mas Amiel Maury Rouge 1985 emerged from a demijohn through an implement which looked disconcertingly equipped to inseminate cattle. Forty-one years old, extracted with the bedside manner of a farm vet.

Meanwhile, alcohol-free pairings treated diners as adults: homemade carrot and rooibos, pine needle, tomato and fig leaf; woodruff, apple and cep. A third star would look less like a favour than administration catching up.

We arrived before our room was ready. This is normally when a hotel produces a sofa, coffee and a sentence involving ‘shortly’. Markus, one of Nimb’s concierges, had a better idea: ‘Would you like to ride the rollercoaster while you wait?’ Ten minutes later, my eight-year-old daughter, Lyra, and I were inside Tivoli. It was luggage storage as an itinerary.

Nimb Hotel, an SLH Hotel, stands within Tivoli’s Technicolor gardens, which brought the world to the city. Its white Moorish building, inaugurated in 1909, takes its name from restaurateurs Vilhelm and Louise Nimb. Our art-rich Junior Suite looked across Tivoli; guests enter freely and receive unlimited rides.

At dusk, ride Rutschebanen. Running since 1914, it is among the world’s oldest surviving wooden rollercoasters, with a brakeman aboard each train controlling its descent by hand. Nazi collaborators burned sections of Tivoli on 24 June 1944; the rollercoaster reopened 25 days later. It now clatters through its painted mountain with the confidence of a machine which has seen off several official systems.

Four days before we arrived, Tivoli opened Hikari, a Japanese-inspired street beneath The Demon. The new Typhoons Eye spins riders towards weightlessness; the relatively genteel Rutschebanen relies on timber and trust.

Nimb also runs The Pagoda in Tivoli’s Japanese Tower, inviting Michelin-starred restaurants into temporary residence. Diners sit on vintage Hans J. Wegner chairs as dragon boats glide past; Bangkok’s three-starred Sühring was preparing to open. Back at Nimb Brasserie, stuffed quail with bordelaise and Beef Wellington met Njord Sandhøj 2023, a Pinot Noir Précoce grown near Holbæk in western Zealand and drawn from the hotel’s vast vaulted cellar. Danish Pinot can arrive burdened with the obligation to be interesting. This one was simply sublime.

My daughter had unlimited rides, I had serious wine, and neither experience had been sent elsewhere. The grown-up and child itineraries shared a room key.

Between hotels, Copenhagen offered a lesson in appetite and capital.

Beside Tivoli, Ny Carlsberg Glyptotek was born of lager wealth. Brewer Carl Jacobsen channelled Ny Carlsberg’s profits into sculpture, antiquities and French paintings before giving his collection to Copenhagen. Beyond its red-brick exterior, marble emperors, Egyptian figures and Rodins gather around a domed Winter Garden of palms and warm light. A laughing girl sculpted by Jean-Baptiste Carpeaux stays with me, mouth open, her teeth rendered with almost dental precision.

A century later, Danish medicine pays for growth. Global demand for Novo Nordisk’s diabetes and weight-loss drugs, Ozempic and Wegovy, helped the pharmaceutical sector account for more than half of Denmark’s 3.5 per cent GDP growth in 2024. The irony is almost indecent: as Danish drugs taught the world to eat less, Copenhagen’s restaurants taught it to eat better.

We checked into 1 Hotel Copenhagen on its first birthday, when staff were handing out cake. It occupies Daells Varehus, the department store founded in 1910, moved here in 1912 and rebuilt in functionalist form by Vilhelm Lauritzen and Fritz Schlegel. According to our tour, the store installed Denmark’s first escalator before its Christmas catalogue reached half of Danish households during the 1960s and 1970s. The building has moved from selling the domestic dream to selling sleep.

The fit is unusually exact: a sustainability-led hotel brand in a city which made environmental thrift a civic habit before hospitality discovered the press release. More than 1,500 plants grow around a timber staircase rising through rock into a double-height atrium. Gardeners shake the larger trees each morning to mimic wind and strengthen roots. Occasionally a meeting receives autumn.

A bee hotel in the courtyard supports pollinators among herbs; local honey appears at breakfast. Our 92-square-metre Flora Terrace House had two bathrooms, living and dining areas, broad balconies and the hotel’s only private sauna. Lyra acquired a knitted bee and the run of the sitting room; we acquired doors.

The Latin Quarter puts the Round Tower, Botanical Garden and old centre within walking distance. Nimb gives you Tivoli; 1 Hotel gives you Copenhagen itself.

Within the hotel, PÆRE takes its name from the Danish word for both pear and lightbulb. The hotel has already moved from Fjora’s Nordic cooking to coastal Italian dishes using Nordic ingredients. This is useful in a city which hardly lacks people willing to explain a leaf.

After nine years in London, Director of Bars Marco Grisafi brought a Negroni Trolley costing the price of a car, spanning classic, lemon, mezcal, coffee and amaro. Agostino ‘Ago’ Perrone of The Connaught Bar later took over the terrace for an evening of martinis. Breakfast citrus and apple return as house gin; spent coffee grounds supply bitterness. Here, circularity comes with ice.

Grisafi’s Blue Cheese Martini combined vodka, Tio Pepe Fino, pear eau-de-vie and blue cheese. Pale, dry and uncompromising, it had no interest in being liked by everybody. He invited Lyra to help at the trolley before making her an alcohol-free cucumber daiquiri. Fritto misto, strozzapreti with red prawns and properly Pecorino-driven cacio e pepe translated PÆRE’s coastal-Italian turn into dinner.

Fifteen years ago, I came to Noma with Signe Bindslev Henriksen and Peter Bundgaard Rützou of Space Copenhagen, creators of its interior. A waiter from Lewisham explained that Noma’s rise to No. 1 on Restaurant magazine’s list had brought a surge of private-jet arrivals and diners who had never fried an egg. He then handed me an insistently beeping timer and instructed me to cook mine in hay oil on a raging iron.

This time, Signe took us through newer work. Esmée has recast the former Geist address, also by Space Copenhagen, as a wood-fired Mediterranean brasserie. Even the stone floor was replaced; a heated terrace extends the season. Staff call Signe ‘As Sortes’, after her favourite wine, Rafael Palacios’s Godello from Valdeorras.

At Kinyobi, a Japanese restaurant and vinyl bar conceived because Copenhagen lacked anything akin to Hakkasan, existing textured stone pillars anchor low furniture and suspended counters, arranged so every table feels like the best. Casino, between the King’s Garden and Round Tower, will combine a delicatessen, ceramics, embroidered curtains and a terrace which changes character through the day, when city bureaucracy permits it.

Her concern with AI was sameness: restaurants assembled from the same digital soup until every room resembles the next. Noma once appeared capable of explaining Copenhagen; her newer work shows why no single dining room can do so now.

On our final night, Radio sat opposite Radiohuset, the former Danish Broadcasting Corporation headquarters which gave it a name. Opened in 2011 by Noma co-founder Claus Meyer and former Noma sous chef Jesper Kirketerp, it was devised to transmit Danish seasonal cooking to a wider audience. Today, with a Michelin Bib Gourmand, it remains one of Copenhagen’s strongest-value serious dinners.

In August, newly promoted head chef Vanessa Barradas put vegetables at the centre. Ten diners withdrew on discovering there would be no meat, efficiently identifying those who did not deserve the menu.

Barradas, from Caracas, moved to Copenhagen a decade ago. Roasted-tomato gazpacho came with strawberries dehydrated, then restored with tomato, vanilla and lime. Fermented carrot met grilled cucumber, crisp fava beans and Søtofte yoghurt. An arepa carried Funga Farm mushrooms and corn sauce in a nod to Venezuela; a courgette tart with Hyrden cheese and tarragon tasted of summer nearing its final page.

Cauliflower took the main-course role without seeking permission, charred and joined by crisp potato, grilled apple, blackcurrant and chilli-spiked Choron. An off-menu spoonful of caviar over cheesecake ice cream provided a surprise departure from the vegetable menu; Barradas sent Lyra an additional helping.

GM and sommelier Frej Sayers, who has Berkshire and Stoke roots, took charge in December and often covers the entire front of house himself. On our evening, chefs delivered dishes while Sayers poured, explained and shook a whisky cocktail threaded with smoked apple.

His list favours family growers, organic and biodynamic farming, and acidity fit for vegetables. The sharpest match was orange Pecorino with carrot, cucumber and yoghurt: its acidity cut through the dairy, while Sayers noted that Pecorino names both the Abruzzese grape and an Italian sheep’s-milk cheese.

Radio’s value comes not from abbreviated cooking or diminished hospitality, but from concentrating both. Its signal is remarkably clear: exact cooking, vivid produce and no static.

The Little Mermaid may remain Copenhagen’s compulsory image, but she is a poor summary of the city: small, exposed, mobbed and marooned at its edge. Follow her gaze inland - into the Glyptotek’s palm-filled Winter Garden, 1 Hotel’s indoor canopy, Koan’s inimitable open kitchen, the joy behind Tivoli’s hedges and Radio’s late-summer vegetables. Copenhagen’s surfaces are lucid; its depths keep opening. At one hour and 50 minutes from London by air, returning is hardly difficult. I shall not leave it another 15 years.