Holmen is the navy's island, just east of Christianshavn across a small channel. The Royal Danish Navy had its headquarters here from 1690 until 1989, and the island is now what happens when a working military base is given over to an architecture school, an opera house, and a film school. The 1748 Mastekran — the wooden masting crane the navy used to step ship masts — is still standing on Nyholm, the cleanest single-object survival.
Three kilometres, ninety minutes. Christianshavn metro lands you a short walk from the bridge onto Holmen. Søkvæsthuset (the 18th-c naval hospital) is the warm-up on the Christianshavn side. Cross the bridge and the Kunstakademi (architecture school) is in the old shipbuilding sheds — the Bauhaus-on-water of Danish architecture training.
Operaen — Henning Larsen's 2005 opera house, marble and glass facing across to Amalienborg — sits on Dokøen. Walk north to Nyholm, where the Mastekran triangulates over the water, a wooden survival from when the navy still rode ships out of here. End back at Nyhavn via the harbour ferry — the opera house from the water is the closing view.