The immense 50 sq km (19.3 sq mi) Askja caldera is as remote as things come in Iceland. Cold, windy and forbidding, the site also provides ample evidence of the creative power of nature. The cataclysm that formed the original caldera happened in 1875, when debris ejected from the volcano made a mess as far away as mainland Europe. Activity continued over the next 30 years, culminating in another massive collapse of surface material. This new depression subsequently filled with water and, with a depth of 217m (712ft), is now the deepest lake in Iceland. Although the lake - a striking sapphire blue - remains frozen most of the year, a smaller and newer crater inside it is still hot and perfect for swimming. Askja is in central Iceland, and is best reached by 4WD vehicle or by organised tour.

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. Apart from the magical line on the map, 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 also 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. After all, failure in chess was failure in life. Enthusiasm for the game has since dampened, but if asked to play, it's best not to treat the occasion too lightly.

Helgafell is the holy mountain that figured so prominently in Icelandic history and literature. In reality, it's a 73m (240ft) hill, yet it apparently still retains some of its magic, and those who follow a few simple rules while climbing it are entitled to have three wishes granted. First, you must climb the southwest slope to the temple ruins without speaking or glancing backwards. Second, the wishes must be for good and made with a guileless heart. Third, you must descend the eastern slope and never reveal your wishes to anyone. Helgafell is 5km (3mi) south of Stykkishólmur, in west central Iceland.

The Jökulsárgljúfur National Park (the name means 'glacial river canyon') is Iceland's newest reserve. Sometimes referred to as 'Iceland's Grand Canyon', the park possesses the country's largest gorge, luxuriant vegetation, bizarre rock formations and caves, the steep-walled valley of Ásbyrgi and myriad waterfalls. Other highlights include the echoing rocks, Hljóðaklettar; the lush and lovely springs of Hólmatungur; and Dettifoss, Europe's most powerful waterfall. The park is east of Húsavík, in northeast Iceland.

The name Kerlingarskarð means 'witch pass.' According to legend, this eerie place was haunted by a female troll until she turned into a stone pillar at the foot of Kerlingarfjall, the mountain that forms the east side of the pass. Nearby is a lake, where the witch is believed to have fished. In the 1800s, a local resident reported seeing huge tracks leading into the water, and a number of sightings of Loch Ness-style creatures have also been reported. If you dare, it's possible to camp and explore around the lake, but the weather is often abysmal. Buses between Reykjavík and Stykkishólmur travel through the pass.