Nyhavn
The canal of painted eighteenth-century houses that appears on every photograph of the city, dug in the 1670s as a working harbour so cargo could reach the centre. It was a sailors' district with a bad reputation for most of its life. Hans Christian Andersen lived at three separate addresses along it.
Christiansborg Palace
The seat of parliament, the supreme court and the prime minister's office, which makes it the only building in the world housing all three branches of a country's government. It has burned down twice. Underneath, the excavated ruins of Absalon's twelfth-century castle are open to visitors, several metres below the current floor.
Rundetårn
A seventeenth-century observatory tower climbed by a spiral ramp rather than stairs, wide enough that a horse and carriage could be driven to the top and reportedly were. The ramp exists because instruments had to be hauled up. It is still a working observatory, and the oldest in Europe still in use.
Tivoli Gardens
An amusement park of 1843 sitting in the middle of the capital, immediately outside the main railway station. Its founder is said to have argued that a people who amuse themselves do not concern themselves with politics, which is a strikingly cynical origin for somewhere so pleasant. Walt Disney visited before building his own park.
Amalienborg
Four near-identical rococo palaces facing each other across an octagonal courtyard, and the royal family's actual home rather than a museum. They were built for four noble families and bought by the crown after Christiansborg burned. The changing of the guard happens whether or not anyone is watching.
Church of Our Saviour
A baroque church in Christianshavn with an external spiral staircase winding up the outside of its spire to the top. You climb it in the open air, and the final turns are narrow enough to be genuinely unpleasant in wind. The architect is the subject of a persistent local story about jumping from it, which is untrue.
Christiania
A self-declared autonomous community occupying a former military barracks since 1971, with a long and unresolved relationship to Danish law. It is neither a tourist attraction nor entirely not one. Photography is restricted in parts of it and the restriction is taken seriously rather than posted decoratively.
The Little Mermaid
A bronze statue of 1913, about 125 centimetres tall, commissioned by a brewer after he saw a ballet of the Andersen story. It is small, close to the shore, and the most reliably disappointing sight in Scandinavia. It has been decapitated more than once and repaired each time.
Rosenborg Castle
A Renaissance summer house built by Christian IV, now holding the crown jewels in a basement treasury. Christian IV built compulsively across Copenhagen and much of what looks characteristically Danish in the old city is his. The garden outside is where the city goes when the weather permits, which is not often.