If you need a break during your sightseeing, or before or after a visit at cinema Imperial - Kop Amok serve a great cafe latte. The cakes are nothing special. Staff is friendly and service minded.
We liked the choices of coffees, pastries and cakes. Prices are reasonable for (expensive) Copenhagen.
It's a nice touch to get a free chocolate covered almond with your cup of caffeine in the morning, which is just one of the reasons I visited this café several times during my stay in Copenhagen. The atmosphere is pleasant, and the pastries are divine (get the chocolate croissant -- you might as well just order two at the outset to save yourself the embarrassment of going back to the counter). There is also free Wifi, so it makes for a great place to take a rest and plan your next move as you travel. My co-travelers also spoke highly of the lattes.