My recommendations would be Christiania, the swimming area at Islands Brygge (where you can take a dip in the cool, clean salt-water of the Copenhagen channel), or rent a bike and head north along the coast towards the beaches in Klampenborg and beyond, while looking at the magnificent houses along the way.
The folk-pop outfit, formed by singer-guitarist Israel Nebeker and drummer Ryan Dobrowski, has taken two bike tours, playing its music all along the West Coast.