A large, artificial (but very nice) beach out towards Oresund. Lots of sandy beach, but also access to the deeper parts via the piers. Fishing is allowed from October 1st to April 30th - essentially outside the bathing season - and the whole beach can be wade fished.
The whole area is worth a visit just for a walk along the water. It's a popular spot for Copenhagen residents, and on nice weekend days the whole beach is buzzing with life - even in the cold season.
Easily accessible by bus, Metro (subway), bike and car. Close to the airport