Located within the rambling Malmöhus Slott, operating under the broad banner (and one low admission fee) of the Malmö Museer, are three main museums within a museum: the Malmö Konstmuseum, Stadsmuseum and a large, unexpected Aquarium that's popular with younger visitors. Top billing goes to the Malmö Konstmuseum, which features a superb collection of Swedish furniture and handicrafts, plus a vast collection of 19th- and 20th-century Nordic art. There's a cafe and decent museum gift shop too.
The excellent Teknikens och sjöfartens hus is part of the collection but not located within the castle walls: it's about 300m to the west.