Nyhavn is the harbour postcard — the seventeenth-century canal lined with painted townhouses you've seen in every Copenhagen photograph. Amalienborg is the working royal palace, four identical Rococo houses around an octagonal courtyard, the guards changing at noon, the dome of the Marmorkirken (Marble Church) closing the axis a few streets behind.
Two and a half kilometres, seventy-five minutes if you time the guard right. Start at Kongens Nytorv and walk north into Nyhavn — the sunny northern side is the postcard, the southern side is where Hans Christian Andersen actually lived. Walk to the bridge at the far end, then loop back south and cut east into Amaliegade.
The royal palaces face their octagonal Slotsplads. The watch changes at twelve; ten minutes early gives you the railing view. The Marble Church dome closes the axis behind the palaces — Frederik V's 1749 ambition, finished in 1894 after a hundred and forty-five years of funding crises. Loop back to Kongens Nytorv down Bredgade, the street of eighteenth-c noble palaces. King Frederik X has lived in Frederik VIII's Palace since 2010; the family is occasionally home.