At Papirøen (The Paper Island) you find Copenhagen Street Food which is one of the best newer inventions in the Danish capital.
Inside a big warehouse you find all kinds of little stalls selling different kinds of food and beverages - also vegetarian.
Outside deck chairs are placed right next to the water and there are plenty of tables and benches where you can eat your food or drink your coffee.
Prices are very reasonable and the food is great. Lots of organic stuff, food from all over the world and in general high quality.
You can walk to the Paper Island from Christianshavn or you can take a harbor bus from Nyhavn.
For more info visit the website of Copenhagen Street Food.