Officially Jægersborg Dyrehave, Dyrehaven is a forest park and UNESCO World Heritage Site, 15 km north of Copenhagen covering 1,000 acres. The park is noted for its mixture of huge, ancient oak trees and large populations of red and fallow deer. There are many trails around the park — a great mix of woods, plains and grasslands, and views of the Oresund (eastern sea). Some of the highlights include a castle, the Eremitage hunting lodge, and a golf course. There are red gates at various park entrances, including one right next to the S-Bahn station.
One of Copenhagen’s largest runs, the Eremitage Run (13.3k, 8.8 miles) takes place annually in the park.
It’s a 1/2 hour S-Bahn ride to the Klampenborg Station.