Reykjavík boasts all the trappings of a modern European city, dusted over with eccentric Icelandic spirit. Thriving cafes, high-energy pubs and clubs, and a brightly coloured old town with rows of wood-and-corrugated-tin houses cluster together in the compact city centre.
The barren lava fields that surround Iceland's international airport are an eye-grabbing introduction to this near-Arctic island, belched out of the mouths of volcanoes (some still active), awash in midnight sun from May to August, glistening with glaciers, geysers, hot springs and waterfalls.
Mývatn, in northeast Iceland, is considered one of the natural wonders of the world. Although most of the interesting sights are volcanic or geothermal topographical features, the reserve's centrepiece is a lovely blue lake teeming with birdlife.
Thanks to its location in the rain shadow of an enormous icecap, the reserve experiences some of the finest weather in Iceland. Travellers can relax and settle in, spend a week camping, or set out on excursions to the Kverkfjöll ice caves, Námaskaro or the Hverfell crater.
Part of the island of Grímsey, lying 41km (25.5mi) north of the mainland, constitutes Iceland's only bit of territory within the Arctic Circle. The main reason for coming here is to admire the cliffs, which are 100m (328ft) high in some places - perfect for bird colonies that nest on the island.
Grímsey is the home of the most avid chess players in Iceland. Historically, losing a match has often resulted in the blunderer flinging himself into the sea - failure in chess was failure in life. While your life is probably safe if you're asked to play, it's best to treat the occasion seriously.