The Duchess of Cambridge is spending a couple of days in Copenhagen, on a fact-finding trip to learn how Denmark has become a world leader in early childhood development.

This is decidedly a working visit – she’s travelling on behalf of her Royal Foundation Centre for Early Childhood, which was launched in June. Kate posted on Twitter of her visit: “Looking forward to learning from experts, parents and practitioners about Denmark’s approach to early childhood later this month.

“Denmark is a beacon of best practice in its approach to the early years, with a culture which prioritises the best start in life.”

However, we can only hope Kate finds a bit of time between her meetings to explore the city. If she did have a chance to see the sights of Copenhagen, this is what we’d recommend…

1. Snap pictures by the harbour

If there’s one defining image of Copenhagen, it’s got to be Nyhavn – a 17th-century harbour lined with colourful houses and wooden boats. One of Denmark’s most famous exports, Hans Christian Andersen, lived here in the 1800s – giving Kate the perfect excuse to tell her children his tales when she returns home.

Plus, Nyhavn has plenty of cafes nestled along the harbour – great places to soak up the ‘hygge’ atmosphere with a Danish pastry.

2. Ski in the middle of the city

City breaks are all very well and good, but what if you’re missing a shot of adrenaline? Kate’s a keen skier and there happens to be an artificial mountain in the middle of the city, CopenHill (copenhill.dk) – where you can ski and snowboard while looking over the skyline of Copenhagen.

There’s also a climbing wall if you’re after a bit more physical exertion – but if not, there’s always après-ski.

3. Visit a fairy tale castle

It doesn’t get much more picturesque than Rosenborg Castle. The Renaissance building is an intricate piece of Danish history, and has lavish rooms to wander around inside – as well as the Danish crown jewels. It’s worth dedicating a bit of time to Rosenborg Castle, as it is surrounded by serene royal gardens.

4. Enjoy gourmet delights at a food market

If you, like Kate, don’t have much time in a city, one of the best ways to try as much of the cuisine as possible is by heading to a food market. And in Copenhagen, Torvehallerne is a must-visit.

The buzzing food hall can be found in the centre of the city, and is full of fresh seafood, fruit and veg, and vendors selling Danish delicacies like open-faced sandwiches known as smørrebrød.

5. Soak up some art on the picturesque coast

Copenhagen is home to some world-class art galleries, and few are as memorable as the Louisiana Museum of Modern Art (louisiana.dk/en). Situated on the coast to the north of Copenhagen, it’s only 35 minutes from the city’s Central Station by train.

Opened in 1958, the museum was initially meant to be dedicated to Danish art – but it’s now home to works from artists all over the globe, and you could easily spend hours there. One of the modern pavilions is home to the Giacometti Gallery – with statues from the Swiss sculptor – there’s an Instagrammable installation from Yayoi Kusama, and one of the highlights is undoubtedly the Sculpture Park, where pieces from Alexander Calder, Henry Moore and others are set within nature, leading out to the sea.