One of my favorit-spots near copenhagen is Dyrehavsbakken(animal garden hill). They where celebrating 425 years 2008. From the beginning it is about an old spring found by a girl who has lost her way in the woods here. And the fairy tale tells that the spring guided her back to copenhagen again. The kings around here has always allowed anyone to visit the garden for getting healthy water frpm the spring and many inhabitants from Copenhagen went out here during summer for having a picknick and maybe some spring water. This made a lot of jesters and salesmen appearing round the spring for selling food, wine, beer and doing some sketches for anyone who wanted to see. Later on they had to pay a small fee for being able to put tent and stands here. These money where financing a hospital for poor peoples near by. The tradition wiht jelters and different eateries continued during the centuries and you are still able to visit the, nowadays, nice tivoli, restaurants and cafes for free. The food is affordable and you are able to get a lot of different dishes. One popular is their pork with parsley-sauce.
like this one where you can eat as much as you want for about 10£ or 16$.
You may also bring your own package of food or beer if you want to.
To get here the easiest way is by oresunds or s-train from copenhagen and stop at klampenborg station
If you got time and the weather is good then try Dyrehavsbakken, you will not regret it. I got some more pictures on bikedenmark.nu>>>