Copenhagen

Copenhagen's centre is compact and walkable, and two icons anchor it. Nyhavn, the old canal cut into the city in the 1670s, is the picture everyone comes for — a row of tall, brightly coloured gabled houses (one of which Hans Christian Andersen lived in) reflected in the water, lined with cafés and old sailing ships, and the launch point for the canal-boat tours that are the best way to see the waterfront. A few minutes away, Tivoli Gardens, opened in 1843, is one of the world's oldest amusement parks and helped inspire Disneyland. It is far more than rides — landscaped gardens, a vintage wooden roller coaster, open-air concerts, restaurants and, after dark, thousands of fairy lights; it is at its most magical in summer and at Christmas. Between them runs Strøget, one of Europe's longest pedestrian shopping streets, leading past the lively squares of Kongens Nytorv, Gammeltorv and the Round Tower (Rundetårn), whose spiral ramp climbs to a city view.

The Danish monarchy, one of the oldest in the world, has left the city a string of palaces. Amalienborg, the royal family's winter home, is four rococo mansions around an octagonal square, where the changing of the guard takes place daily at noon, on an axis between the harbour's Opera House and the great dome of the Marble Church. The Renaissance Rosenborg Castle, set in the leafy King's Garden, houses the Danish crown jewels and royal regalia in its treasury. Christiansborg Palace on the islet of Slotsholmen — the city's historic core — is the seat of the Danish parliament, with royal reception rooms, stables and a tower (with a free viewpoint) open to visitors, and Viking-and-medieval ruins in its basement. Together with the National Museum nearby, they make a rich half-day of Danish history.

Copenhagen is a world capital of both design and food. Danish design — the clean, functional, timeless aesthetic of Arne Jacobsen, Wegner and Kjærholm — fills the Designmuseum Danmark, the furniture and homeware shops, and the very fabric of the city; even the street furniture and cycle bridges are beautifully made. The food scene is just as celebrated: the New Nordic movement, led by Noma (repeatedly named the world's best restaurant), reinvented Scandinavian cooking around foraging and local produce and turned Copenhagen into a pilgrimage for food lovers, with a dense cluster of Michelin stars. But eating well here isn't only fine dining — the open-faced rye-bread smørrebrød lunch, the celebrated Copenhagen hot dogs (pølser) from street carts, the produce-and-wine market hall of Torvehallerne, and the waterfront shipping-container street-food market of Reffen cover every budget and mood. Both the smørrebrød lunch and the sausage wagon are national institutions with conventions of their own, set out on the Denmark food guide.

Copenhagen's relationship with its water is part of its charm. The harbour is so clean that locals swim in it at the popular Islands Brygge and other harbour baths in summer, and kayaks and “GoBoat” picnic boats ply the canals. Across the water, Christianshavn's canals and houseboats lead to the freetown of Christiania, an alternative, self-governing community founded in the 1970s on a former military site — a green, ramshackle, car-free enclave of murals, workshops and music (with its own well-known rules to respect). The twisting golden spire of the Church of Our Saviour (Vor Frelsers Kirke) can be climbed for a view over it all. Beyond the city, easy train day trips reach Kronborg Castle at Helsingør — Shakespeare's “Elsinore” from Hamlet — the Viking Ship Museum and cathedral at Roskilde, whose five original ships and the wider Viking landscape are covered on the Viking Denmark guide, and the spectacular Louisiana Museum of Modern Art on the coast at Humlebæk; the Øresund Bridge even puts the Swedish city of Malmö about 35 minutes away. Onward travel beyond the day-trip radius is covered on the getting around Denmark guide.