Carlsberg Glyptotek situated close to Tivoli and the main square Rådhuspladsen in the centre of Copenhagen is an excellent art gallery. It’s owned and run by the Carlsberg fund, meaning you are contributing to the arts as you down a nice cold beer.
It has a large collection of ancient Egyptian artefacts, a large collection of Roman statues, and lots of Danish landscape paintings from the 18th and 19th century which are all great collections.
However, what makes the Glyptotek frankly unmissable if you are in Copenhagen, is the collection of Impressionist and Post Impressionist works. There are Van Goghs, an excellent Manet (see below. Check out the black bottle in the bottom corner), Courbet, Degas, Cezanne, Renoir and quite a few Gauguins.
Gauguin lived in Copenhagen for a few years, and was married to a Danish woman called Mette.