The National Theatre of Iceland is the country's main stage, set in a distinctive dark building in central Reykjavik. Its repertoire mixes Icelandic writing with international plays, and it is one of the best places to see the city as a living cultural capital rather than just a gateway to landscapes.
Language matters, of course: many productions are in Icelandic. Still, dance, music, visiting productions, and the building itself can make it worthwhile to check the programme.