We are very lucky in Copenhagen to have such a selection of high quality independent coffee shops and cafes. In fact just today I was eating brunch in one of the popular city centre cafes with a friend visiting from the UK and her nine year old daughter and, after devouring a plate of homemade pancakes with fresh fruit and crispy bacon, her daughter announced that they needed a place like this at home.
One of my favourite cafes in the city centre is in the main library on Krystalgade. Democratic Coffee is an independent coffee shop located on the ground floor of the library. They serve their own coffee blend and amazing croissants and pain au chocolat. The shelves of the cafe hold an eclectic selection of library books for you to enjoy with your coffee (and to borrow later if you wish).
The coffee shop is fairly small but you can take coffees into the lounge part of the library adjacent to the coffee shop. I love the slightly intellectual but unpretentious feel of this place.