Just a little train ride away from the city you find Dyrehavsbakken or just Bakken (The hill) as its normally called in Danish is situated in the southern part of the large forest Dyrehaven. Its the oldest amusement park in the world dated back to 1583 (pls tell me if you know one older). It has a felling like a large version of this travelling fairgrounds or a laidback version of the famous Tivoli, with bumper cars, carousels, tom bolas, rollercoaster rides and so on.
There is no entrance fee to Bakken. For the rides you can buy a wristband for 200 Danish kroner. With a max of teen rides on the particular ride …but more will make you sick (or maybe its just me)
To get there the best way from cph is to take the regional train at the central station in direction towards Helsingør (Ellsinore) after 15 minutes you get of at Klampenborg station. And make a little walk (10 min) or charter a horse carriage.
Bakken is the laid-back version of tivoli. It's not as expensive, but doesn't quite have that very special atmosphere that tivoli has either, especially when it comes to places to eat. It's one of the world's oldest amusement parks, and its surroundings are extremely scenic, as it's in a corner of a large wooded area used for picnics, horseriding and deer watching. Still, you will find that the clientele is very different from the one at tivoli. I suppose this is seen as more of a lower-class version, but I prefer to think of them as different and I like them both.
Bakken is less known than Tivoli and has a totally different atmosphere. It is more laid back and not as fancy. The rollercoaster was very interesting I recall. If you have time it really merits a visit.