Christianshavns Mound
Christianshavns Mound is part of Copenhagen's old defense system. It is now an excellent area for a walk surrounded by green and water, passing a number of historical buildings, cafes and restaurants. Christianshavns Mound was built by Christian IV in 1618-23 and was further developed in the following centuries. The defense purpose ceased towards the end of the 19th century and public access to the area was successively established in 1961.
Kastrup Fort
Another of Copenhagen's old fortifications, which has been turned into an attractive park. Other than the outline, moat, walls and a few buildings remaining, there is not much to see here in terms of history. But there are some nice views over the sound and you can venture into the open part of the catacombs and see bullet holes from Nazi executions during WWII. A stroll here is easily combined with a visit to Amager Strandpark see Do section, but otherwise probably not worth the effort.
Kalvebod Fælled
(http://www.skovognatur.dk...). Something of a peculiarity, Kalvebod Fælled covers 2000 hectares 5000 acres of protected wetlands, beaches, forest, and lakes in southwest Amager, rich in wild-life like birds and deers. Nowhere else in Europe will you find such a large area of wild nature this close to a major city. There are quite a few activities available, like bike rentals, horse riding and lots of stuff for the kids. In the autumn many Copenhageners come here to fly colorful kites.
Kongelunden
(http://www.skovognatur.dk...). If you are staying at a hotel or the camping grounds in Dragør, this small forest is a nice place for a stroll, particularly down Kærlighedsstien, or the path of love in English. A reference to a dancing hall once located down this path, it is long gone, but it is still a romantic place on a nice spring day. If you have kids, the open plains facing the water have grassing sheep the toddlers can chase around.
Kastrupgårdsamlingen
Set in a beautiful old mansion-like country home from the 18th century, this museum displays a large collection of graphics from mainly Danish artists, including a large collection of the somewhat internationally known Cobra artists. There are also a temporary exhibition space.
Dragã¸r
Dragør is a small village south of the airport with a rich navalhistory. The picturesque old village centre is well preserved withcobblestone streets, pretty old yellow buildings with red tiled roofs,and the harbor still has an active fishing port — in essence it is a very traditional Danish village within easy reach from the city centre. To get here either jump on bus 350S which has several stops in downtown or change to bus 35 at the Copenhagen Airport Station. If you are not into the hustle of big cities, you may want to consider sleeping in the historic Dragør beach hotel listed below.
Dragør Museum
A museum detailing the maritime history of the village, including a collection of paintings by famous local artist C.W. Eckersberg 1783-1853, ship models and various quirky items from around the world, brought home by the local sailors. The museum also includes a small art museum, Mølsteds Museum, in the centre of the village, and a fishing vessel used under the famous evacuation of Jews under the German occupation.
Amagermuseet
A historical museum in two old farm houses, detailing the Dutch history of immigration on the island, who were invited to the island by the king to dam and farm the island after the Dutch model. There is also exhibits on historical interiors and textiles.