A Romantic 3-Day Copenhagen Weekend for Couples

Opened in 1843, it is less an amusement park than a walled pleasure garden of lakes, lanterns, flowerbeds, small theatres and a wooden rollercoaster from 1914, all at its best lit after dark. Walk the perimeter slowly, eat something, ride one thing, and let the rest go. It sits opposite Central Station, so it fits either end of an arrival day. One catch: Tivoli closes completely between seasons. When it is open, the Christmas season is the one to aim for.

Take to the water. Canal tours leave from Nyhavn, the gabled, brightly painted quay on every postcard, and show you the harbour, Christianshavn's canals and the opera house from the angle the city was built to be seen from. Some operators run heated, glass-roofed boats through the colder months, so this plan can survive a January weekend, though boats still cancel for weather.

The Church of Our Saviour's black-and-gold helix spire takes around 400 steps, the last 150 on an external staircase that spirals around the outside, narrowing as it climbs to about 86 metres. Thrilling if heights don't bother you; skip it if they do. From the top: the whole city, the harbour and, on a clear day, Sweden. The tower is closed all January and shuts the same day for rain, snow or strong wind. Afterwards, wander Christianshavn's canals, houseboats and low old houses.

Rosenborg Castle is a small Renaissance castle in Kongens Have, the oldest royal garden in the city. The garden is free and always open, its rose garden lovely in summer; the castle keeps seasonal hours and holds the crown jewels in its basement. A gentler afternoon that works in any weather.

Then there's CopenHill, a waste-to-energy plant with a ski slope and hiking path on its roof, free to walk up during opening hours for one of the widest views over the city and harbour. It is the least postcard, most memorable half-day of the weekend. Reffen, the food market, runs roughly mid-March to the end of September before becoming an ice rink; CopenHill works year-round.

SMK, the national gallery, spans seven centuries of European and Danish art, and its permanent collection is always free. The Ny Carlsberg Glyptotek is the more romantic: sculpture around a glass-roofed, palm-filled winter garden, one of the warmest places to sit in January. It charges admission, with free entry on the last Wednesday of each month.