The Bidstrup Forests
The Bidstrup Forests are a mix of hardwood and coniferous forest in a hilly terrain. You can sleep in various shelters i the woods. See the shelters on a map here (Danish)
There are two trekking tracks, one ride track and a track for mountain biking.
Fenced dog area nearby (Storskoven in Hvalsø). Free entrance. Download map (in Danish) here
The woods were given to the citizens of Copenhagen by the King Frederik III as an appreciation of their endeavours during the siege of the city in the Swedish war.