Iceland | Reykjavik
A very comprehensive and interesting place, Iceland's national museum contains artifacts from the Settlement Age to modern day and also has photography and rotating exhibits. It gives a good overview of Icelandic history and culture and is worth the trip if you have an extra day in Reykjavik.
Iceland | West Iceland
This museum in Borgarnes is split into two parts. The first uses multimedia to explore the Settlement period of Iceland. The second explores Egill's Saga. There is an attached restaurant with good reviews.
Iceland | South Iceland
A complex of three museums: an outdoor museum featuring farmhouses from different eras of Iceland's history; a folk museum showing off artifacts from daily life, and a technology museum. Interesting to get a feeling what life in southern Iceland was like.
Iceland | Reykjavik
The Settlement Exhibition details the history of Iceland's settlement through multimedia and surrounds the foundations of a Viking-aged farmhouse dating to the tenth century.