The stretch south of Copenhagen offers a lot of accessible water even though much is sandy and shallow. The area is also known as Køge Bugt (Koege Bay) and stretches all the way to the major city Køge in the south.
You can drive along the southern road Strandvejen (route 151), typically named after each town it passes (Hundige Strandvej, Mosede Strandvej, Karlslunde Strandvej), and drive down to the water several places. There is public parking on several location.
Buses run from Copenhagen along the same road and many have stops close to the water at places like Ishøj Strand, Hundige Strand and Mosede Fort.