Copenhagen

The 17th-century harbour of gabled houses painted every colour, old wooden ships on the water and cafés along the quay — the image of Copenhagen, and where Hans Christian Andersen lived. Touristy and worth it; grab an ice cream or a beer on the quayside and watch the boats.

The enchanting 1843 pleasure garden in the middle of the city — vintage wooden coaster, lantern-lit gardens, concerts and old-world rides that inspired Walt Disney. Magical after dark, and unmissable when it's dressed for Halloween or Christmas.

The small bronze of Andersen's heartbroken mermaid on her rock in the harbour — famously, and cheerfully, underwhelming in size, but a rite of passage all the same. Pair her with a walk through the Kastellet star fort and along the waterfront to the royal quarter.

A self-governing commune founded by squatters in an old barracks in 1971 — car-free lanes, homemade houses, murals, music and workshops, a genuinely singular corner of the city. Wander, eat at a café, respect the no-photo rules on Pusher Street; there's nowhere else like it.

One of Europe's longest pedestrian streets, threading the old town from the city hall to Nyhavn past squares and shops — and just off it, the 17th-century Round Tower you climb by a spiralling ramp for a view over the rooftops. The city's walkable spine.

A fairy-tale Renaissance castle set in the King's Garden — the royal treasury in its cellar glittering with the Danish crown jewels and regalia. Small, rich and central, wrapped in the loveliest park in the city, where all Copenhagen sunbathes in summer.

The rococo palace where the Danish royals actually live — four mansions around a cobbled square, with the bearskin-capped guard marching in daily from Rosenborg and changing at noon. Line it up with the domed Marble Church looming behind for the grand set piece.

Climb the corkscrew spire of this baroque church in Christianshavn — the last 150 steps spiral up the outside, on a gilded staircase, to a dizzying view over the whole city and harbour. Not for the faint-hearted, and the best panorama in Copenhagen.

Copenhagen's night out — the white-tiled old meat market in Vesterbro, now packed with buzzing restaurants, natural-wine bars and clubs that run late. Cool without trying too hard, and the best-value good eating and drinking in an expensive city.

Two glass food halls by Nørreport packed with the best of Danish eating — smørrebrød, fresh fish, cheese, coffee and pastries, plus stalls to eat at on the spot. The tastiest, most affordable way to graze your way through new Nordic food.

Denmark's open sandwich raised to an art — dense rye piled with pickled herring, roast beef and crispy onions, or prawns and dill, eaten with a cold beer and a shot of aquavit. The classic Copenhagen lunch; do it properly at an old cellar restaurant.

The harbour is so clean you swim in the middle of the city — dive off the wooden decks at Islands Brygge, right by the centre, alongside the locals on a warm day. A gloriously Copenhagen thing to do, and free; just check the flag is up.

Do as the Danes do and get on a bike — the flat, cycle-first city is made for it, and a loop around the willow-lined Lakes and over the buzzing Dronning Louise's Bridge into Nørrebro is the loveliest, most local ride. Hire one for the day and never look back.

The home of the thing Denmark does best — a beautiful museum of Danish design, from the iconic chairs and lamps you'll recognise to a whole hall of them, in an old rococo hospital near the palace. Essential for anyone who loves how this country makes things.

Not morbid but beloved — a leafy walled cemetery where Copenhageners picnic and sunbathe among the graves of Hans Christian Andersen and Kierkegaard, in the heart of hip Nørrebro. Wander it, then dip into the quarter's wine bars and vintage shops.