Amager Strandpark is Copenhagen's beach — two kilometres of artificial sand opened in 2005, walkable end-to-end, with a central lagoon for the families and Kastrup Søbad (the wooden Snail) a few kilometres south for the architecture pilgrimage. The whole stretch is metro-accessible from the city centre.
Four kilometres, a hundred minutes if you walk the full length. Start at Amager Strand metro (M2 line, twelve minutes from Kongens Nytorv). The beach is across the bridge — Copenhagen's only proper beach, fronting the Øresund. North end first if you want grass and pines; south end for the lagoon and family stretch.
Walk south along the sand. The central lagoon is enclosed, calmer, better for small swimmers. Continue past the Helgoland swim bath (the 1913 wooden complex) and onto the coastal path — the architectural prize is two kilometres further at Kastrup Søbad.
Kastrup Søbad — the Snail — is White Arkitekter's 2005 wooden swim circle, a coiled walkway and platform raised over the sea, distinct from any other swim spot in Denmark. Free, open year-round. Kastrup metro is five minutes inland for the M2 back.