Amalienborg PalaceHome of the Danish royal family, four palaces set around a square. The daily changing of the guard takes place around noon. Part of it is a museum (free under 18), and the square itself is free.
Rosenborg CastleA Renaissance castle in the King's Garden, holding the Danish crown jewels in its basement treasury and royal rooms above. Combine it with a run around the garden and its dragon playground. Free under 18.