It doesn't look like much, but this tiny kebab shop just off of Sankt Hans Torv is a great spot to get a kebab. Also, if you look closely at the counter you'll see that it is decorated with passages from Machiavelli's Prince.
Made famous by the Turkish district in Berlin, kebabs are a Copenhagen specialty and Dane's go-to budget food. For those unfamiliar, they are similar in form and shape to what most Americans would call a Greek Gyro. More accurately named based on their size pitabrød (small) or durum (large) but loosely called "kebabs" these takeout restaurants offer beef, beef/lamb, chicken, or falafel variations. Quality, price, and flavors vary widely. With different vendors using different types of chili, yogurt sauce, lettuce, tomato, and various other fixings.
While you can find kebab shops (which also often serve pizza) all over Copenhagen the highest concentration is along Nørrebrogade in Nørrebro between the lakes and the area two blocks north of Nørrebro station.