The King's Forest is actually a forest, but this refers to the beach on the southwestern part of Amager, often called Kongelunden too. The beach is sandy and requires waders to fish (or surfcasting gear), and the water is very shallow and allows for wading far away from the shore.
It can hold garfish in the season, sea trout and ide.
The location can be reached from Copenhagen center in 15 minutes by car and there's a large public parking space. Bus line 33 stops withing a short walking distance of the beach.