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With the exception of Húsavík in the north, Reykjavík is actually one of the very best places to go whale watching in Iceland. Whales frequently come into Faxaflói, the large bay which Reykjavík sits by and on a typical trip of around 3 hours you can almost be guaranteed to see at least some minke whales and possibly even a humpback. The companies offering whale watching mostly occupy a small area in the old harbour called Ægisgarður, close to the whaling ships. All sail out to the same bay but since conditions there change make sure you are on a good ship.
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Ljósmyndasafn Reykjavíkur
A very small museum with a nice library and reading room where you can find some older (but good) books about photography and current and past issues of photography magazines. It also has a huge collection of Icelandic photographs.
By the old harbour in Reykjavík, Hafnarhúsið hosts a rotating exhibitions of the work of Icelandic artist Erró and temporary exhibitions often showcase other local artists.
The new home of the Icelandic Symphony Orchestra and regularly host to other acts as well. Delayed by the economic collapse, this building was under construction for several years before finally opening in May 2011. This marked the end of a long wait for the symphony orchestra, who had been using a cinema as their main venue the last 50 years. Today the symphony plays a concert every Thursday evening from September through June (although often at other times as well), but the building is rarely empty at other times with Iceland's lively music scene having embraced this new location.
The Settlement Exhibition
Run by the Reykjavík City Museum, this exhibition in central Reykjavík was built around the oldest archaeological ruins in Iceland. As the name indicates, these ruins date to around the year 870. This interactive exhibitions brings you the early history of the area that today forms central Reykjavík.
A small park (or square, depending on definitions) in the heart of Reykjavík. It's many locals' favorite place to spend sunny days, either at one of the cafés lining the north of the square or simply having a picnic on the grass. The parliament and the national cathedral both stand by Austurvöllur.