Statens Museum for Kunst is Denmark's national gallery, with all the privileges that entails. The collection has an extended collection of Danish and other western artwork dating from the 14th century till today. This means it covers old and contemporary works.
Located inside a historic building, the museum even has workshops of art related activities for children. Thanks to Johannes Rump's generous donation almost a century ago, the National Gallery of Denmark now houses a large collection of early French Modernist paintings. Its ethnographic, Asian and Inuit collections are also interesting. The museum also hosts other temporary exhibitions, such as the Matisse Collection, which was on at the time of visit. Allow yourself a couple of hours for this one.