All along thisuninhabitedshoreline, sea islands, salt marshes, andsandy beachesprovideaperfect resting place forTundraswans, coots, gallinules, and otherwater birds.
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.