This fantastic collaboration between the National Museum, National Gallery and four other organisations creates a superbly curated exhibition covering the artistic and cultural heritage of Iceland from settlement to today. Priceless artefacts are arranged by theme, and highlights include 14th-century manuscripts, contemporary art and the skeleton of a great auk (now extinct). Check the website for free guided tours.
The renovated 1908 building is beautiful with great views of the harbour and has a classy cafe on the ground floor. Entry also covers admission to the National Museum.