There are so many, so we only mention a few:

Old city:
Kreutzberg,
The Cafe Next Door.
The Log Lady.
La Glace. (best Danish pastry and cakes in town)
Kafferiet.
Cafe Flottenheimer, Skindergade.
Nutid, Nørregade.
Kalaset, Vendersgade.

Christianshavn:
Månefiskeren (Christiania – smoking)
Parterre.
Wilders.
Sofie kælderen:

Nørrebro:
Cafe Blå. (Vegan)
Tjilipop.
Laundromat.
Coffee Collective.
Probs.
Bevars.
Cafe Goodlife.
Kimia.
Mahalle.
Friheden.

Vesterbro:
Sort Kaffe og Vinyl (Also a record store)
Bang og Jessen.
Kioskh.
Mother.
Cafe Dyrehaven.
Stempel Bar.
Absalon kirken.
Cafe Mandela.
Cafe Snorks.
Beat Cafe (Also a record store)