Because we have no unpacking to do, we head straight out to explore the neighbourhood on foot. Cyclists whizz along the wide bike lanes bordering each side of the road. About half are cargo bikes with large buckets on the front to transport goods or people — and not only children.

Denmark’s welfare state and widespread cycling contribute to its high happiness rankings. Photo / UnsplashDenmark’s welfare state and widespread cycling contribute to its high happiness rankings. Photo / Unsplash

“Look, a bike shop!” my companion says. We go in, check out rental costs and look at helmets, in case our bikes don’t arrive today. Fifty metres down the road we spot another cycle shop and go into that one too. Then, as we keep walking, we see another, and another, until we realise there’s a bike shop on every block. Most are functional, aimed more at servicing than accessories.

There’s no sign of our bikes by the next morning, so our friends advise us to use one of the on-street cycle hire apps. We hire bikes for three days, picking them up from the corner of our street. The bikes have names: mine is December, my birth month, while my companion has Buster, the name of an old friend. It seems like a good omen as we set off on our tour of Copenhagen. The bikes are the upright Dutch style with big baskets on the front and are a blast to ride.

Biking in Copenhagen is so popular that nearly 50% of its residents commute by bike. Photo / Getty ImagesBiking in Copenhagen is so popular that nearly 50% of its residents commute by bike. Photo / Getty Images

Copenhagen is small and we ride with no planned itinerary, without fear of getting lost. We end up near the Little Mermaid statue, which is rather underwhelming. Tourist buses disgorge people who crowd around it, taking selfies in front of the tiny, forlorn figure on her rock.

“Is that it?” asks my companion.

“Yep.”

“Let’s get out of here.”

The Little Mermaid statue. Photo / 123rfThe Little Mermaid statue. Photo / 123rf

We ride past the statue of Denmark’s most famous writer, Hans Christian Andersen, clad in a top hat and frock coat, holding a book — perhaps The Little Mermaid? — and staring wistfully at the sky.

As we ride around the city, beautifully dressed people, some in skirts, dresses and heels, power past us. We’ve been in the same clothes for two days, so we decide to buy something to wear in case the bags don’t turn up tomorrow. I choose a blue T-shirt picturing a bearded man with a sword riding a bike.

“Ah, the Biking Viking,” says the shop owner. “That’s very popular.”

On day three, our luggage still hasn’t arrived, so we head out again on Buster and December. Then Norwegian Air rings, telling me our bags have been found. We buy celebratory coffee and raisin buns, which we consume in a traffic-free garden square. Afterwards we ride through the port area, which has been transformed from a military base into a nature reserve criss-crossed with walking and biking lanes.

Danish pastries are famous in Copenhagen. Photo / Getty ImagesDanish pastries are famous in Copenhagen. Photo / Getty Images

The next morning, we check our hire bikes in and head out on our Bromptons. At pretty Rosenborg Castle, previously a royal residence, we look around the grounds and the shop. I buy a postcard and ask the cashier if they sell stamps. He tells me Denmark no longer uses stamps — you have to go online, get a code and write it on your mail.

 Rosenborg Castle. Photo / 123rf Rosenborg Castle. Photo / 123rf

“It’s efficient, but it doesn’t have the same appeal as an actual stamp does it?” I say.

“No! It’s not so charming.”

For lunch, we visit a pastry shop, which is packed with slim people eating cakes. We have rye sandwiches stuffed with cheese, hummus, salad and gherkins. For dessert, my companion has a wienerkrans — a light confection filled with toasted hazelnuts — and I choose one stuffed with rhubarb and marzipan.

To work off the cakes, we cycle to Churchill Park, home to the Danish Resistance Museum. A procession of horse-drawn vehicles rolls past: an old Carlsberg wagon driven by men in white shirts, top hats and black aprons; braided ponies harnessed to traps carrying smartly suited people; men in flat caps on rustic milk wagons pulled by carthorses. In the evening, we hear a hubbub outside the apartment — a long train of rollerbladers and skaters lit up with reflectors, lights and fluoro snakes around the lakes. There are lots of ways to roll in Copenhagen.

Though Copenhagen is tiny and you can see it in three days, there are plenty of museums to keep you occupied on a longer trip. On our final day we go in search of Vikings at the National Museum of Denmark. If you’re in Copenhagen on a Wednesday, lucky you — museums are free. This being Tuesday, however, we have to pay. But it’s worth it — there’s lots to see and entry includes free guided tours. We take the Viking tour. The Viking halls are mind-blowing, with artefacts ranging from a tiny gold ship on a razor to the remnants of the longest longship ever discovered, at 37.4m. It was found in nearby Roskilde Harbour when the site was excavated to extend the Viking Ship Museum. Staff were planning to build a replica ship right where the real one was found.

Strolling down colourful walkways. Photo / UnsplashStrolling down colourful walkways. Photo / Unsplash

We join another tour of the 20th and 21st-century galleries; the guide talks about Denmark’s high rates of happiness, which he attributes to the welfare state and widespread use of the bicycle. I think it’s also the pastries. We’re in the museum almost all day, so I run out of time for the Ib Antoni exhibition at the Copenhagen Museum. There’s just time to visit the gift shop and buy some items featuring the work of the iconic designer who created the post-war Wonderful Copenhagen tourism advertising campaign. As I pay for my tea towels and fridge magnets, the cashier tells me if I’m here on Wednesday, entry to the museum will be free. “Sadly, I leave tomorrow,” I say.

And I am sad. Because I’ve fallen in love with Copenhagen, with its bikes, pastries, and friendly, happy people.

ChecklistCOPENHAGEN

GETTING THERE

Emirates, Qatar Airways and Air NZ, in codeshare with Singapore Airlines, all fly from Auckland to Copenhagen with one stopover.

DETAILS

visitcopenhagen.com