Reykjavik Museum of Photography has around five million photographs from the years of 1870 to present date and has quite the extensive registration of them. The staff is highly knowledgeable and they always have coffee in the kettle. They always have some interesting exhibitions open for public.
If you want to experience Reykjavik (or Iceland in general) in the past, then this might be a nice start. For postcard collectors this might be the catch of the day and for general history buffs this is a goldmine. The museum is considered to be one of the best free museum in the world, according to the Guardian.
The Hollywood superstar Viggo Mortensen donated a lot of his published books to the museum and they are available for good price.
Mon-Th: 12:00-19:00
Fr: 12:00-18:00
Sa-Su: 13:00-17:00