Reykjavik City Museum: Two sites, both excellent
The Reykjavik City Museum operates an open-air museum (Arbaer Farm) in the farther reaches of the city, and a downtown exhibition just around the corner from the Radhus (City Hall). The in-town one is called Reykjavik 871±2, and is an excavation of an early Viking hall, or residence.
The Arbaer Farm site, based on a farm that operated there for several hundred years, up until 1947, has been a museum since 1956, and a number of other buildings from around the city and a few from elsewhere have been moved there. In summer, there are historical interpreters on hand, and most of the buildings are open; in winter (our visit) there is a daily hour-and-a-half guided tour by a very knowledgeable young docent. The tour includes a rural church, the original Arbaer farm house with its built-on extensions for cooking, animals, etc., a Reykjavik house from the early 1900s and a shed with fire-fighting equipment and one of Iceland's only two locomotives ever.
The farmhouse and church are both built mainly of sod, together with some stone and wood. The farmhouse part of the tour was especially interesting because of the variety of roles that involved the farm families and their employees over time, and the changes over the last century or so of its working life. The building looks quite small, but actually extends through ells and wings to be bigger than you'd think.
The downtown exhibit, also called The Settlement Exhibit, consists of the floor and part of the walls of a Viking longhouse or hall that would have been the center of a sizable family's life shortly after settlement. The date in the exhibit's name refers to a major volcanic eruption that occurred a few years after settlement; because it can be fixed in time to that period, the age of the hall is known because it is sitting on top of ash from the eruption; an adjoining animal pen that is part of the excavation i known to be older because it extends below the "settlement layer." The excavated area is surrounded by exhibits and narration that explain the lives of the early setters, including their origins and what we know of their culture (an issue with still unsettled scholarship). There is also a reconstruction in scale of what the hall would have looked like. The survival and excavation of the hall owe a lot to Reykjavik's very late development as an urban area, and the ongoing subsidence of land; it was found 2 meters below the 20th century street level.