A small lake with free fishing, easily accessible at the end of the Metro (subway) line towards Amager Fælled. The whole Amager Fælled area is well worth a visit and easy to access using the metro or a car. No cars are allowed in the area, but on a bike you can even ride inside the fenced area, which has grazing cattle (behind further fences) as well as a lot of birds, plants and nice sights - just 15 minutes away from the town center.
Several lakes in the area has public fishing access as can be seen on this (Danish) folder from the Danish Nature Agency. The small fish symbols on the map indicate that fishing is allowed. A state license is still required of course.
By car or bike via Kanovej or with the Metro to the Vestamager station. From there it's a short walk to the lake.
