Denmark's national gallery, with Danish and international art from the 14th century to the present. The permanent collection is free. The Danish Golden Age rooms are exceptional.
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The Danish Golden Age collection (19th century): C.W. Eckersberg, Christen Kobke, L.A. Ring. These painters documented Danish light and landscape in a way that remains the best visual record of the country. The international collection includes Matisse, Picasso, and a good French collection.
Weekday morning for the permanent collection. Free admission to the permanent collection means it's an excellent option even for short visits.
The Danish Golden Age painters are the reason to visit SMK even if contemporary art is your focus — Eckersberg and Kobke painted Danish light with a specificity that makes you see the country differently. Free permanent collection. The building (1896, expanded 1998) is worth noting architecturally. Near Rosenborg Castle for combining into a Kongens Have morning.