If you are looking for somebody who lived and worked in Copenhagen, then the answer got to be Vilhelm Hammershøj (1864 - 1916), whoes interiors are quite famous.
http://en.wikipedia.org/wiki/Vilhelm_Hammersh%C3%B8i
If we are talking about just anybody painting in Copenhagen in shorter periods, then then french painter Paul Gauguin should be mentioned. Because he was married to a Dane he produced a number of paintings from Copenhagen i the 1880's e.g. from the Citadel.
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Roberto Matta.
Cranach
I believe it was Miro.
david Boyd is a famous Australian artist and painter who was painted heaps of paintings
Leonardo DaVinci was the famous painter; Bach and Beethoven were famous composers.