Walked by this place many times during a visit, and there was ALWAYS a line at the window. For a hot dog stand? Yes! And they were delicious.
From Wikipedia: "...operating since 1937. In August 2006, the British newspaper The Guardian selected Bæjarins beztu as the best hot dog stand in Europe. It is believed that the majority of Icelanders have eaten at Bæjarins beztu. Foreign visitors are often brought to the stand by locals to introduce them to the hot dogs there, which are often called 'the Icelandic national food.' "