Islands Brygge is the southern harbour-bath Copenhagen — Havnebadet, the 2002 Plot/JDS-designed wooden swim platform that made Copenhageners realise the cleaned-up harbour was actually swimmable, opened the floodgates for the half-dozen swim spots now strung along the inner harbour. The walk covers Islands Brygge's stretch and pushes south to Sluseholmen for a second swim if you want.
Three and a half kilometres along the water — summer only, May through September when the swim baths are open. Start at Islands Brygge metro (M1/M2) and walk west to the harbour edge. Havnebadet is the famous one: long wooden deck, ladder-and-platform pools, lifeguards in summer.
Walk south along the harbour path. Bryggebroen (the pedestrian-cycle bridge) crosses west to Fisketorvet if you want the detour. Sluseholmen's swim bath is the southern endpoint, fifteen minutes further along — newer, less crowded, the canal-and-lock architecture giving the swim a different feel.
Walk back to Islands Brygge or grab a bus. The newer Nordhavn-side swim spots like Sandkaj are an entirely different walk — see the Nordhavn route for that side of the harbour.