Reykjavík is a small town by anyone's standards. Capital of a country the size of England and Wales together, the city comprises approximately 40% of the country's meagre population of 280,000, making it the island's only real city and the cultural centre of everything in Iceland. The attractions of coming here are twofold: for the countryside within easy reach of the city, alive with geological faults; and for the lifestyle in the city, young, vibrant and earth-shaking in its own way.

Laugardalur Valley and Öskjuhlíð Hill

On the outskirts of the city you'll find two of Reykjavík's most idiosyncratic sights. Laugardalur Valley is the centre of Iceland's sporting activity and a bit of a hotspot. The name refers to the hot springs, now used to feed the city's biggest swimming pool, with steam room, Olympic-sized outdoor pool and a number of hot pots. Öskjuhlíð Hill has got the look of a secret military hideout built on the foundations of an old Second World War base, but the spherical Pearl building was not designed to be hidden, perched as it is like a broody hen, on top of six round tanks that store the city's hot water. It's the nearest thing the city has to the Eiffel Tower, with viewpoints out over the city and beyond, and a nice café inside. At the very top there's a revolving gourmet restaurant and a fabulous bar, but both are prohibitively expensive even by Icelandic standards. Down at the foot of the hill you'll find a yellow- sand beach, hot pots and a warmed-up section of the Atlantic that you can swim or paddle in.

Hafnarfjörður and the Blue Lagoon

On the Reykjanes Peninsula to the west of Reykjavík are two sights that make use of the natural surroundings. The dark, bumpy, moss-covered lava fields around Hafnarfjörður in particular have given rise to numerous stories about elves, pixies and angels, and a reputation for being home to the biggest otherworldly community in the country. And beyond it towards Keflavík is the world-famous Blue Lagoon, a steaming pool of opaque turquoise water that leaches minerals from the lava bed, filling it with healing properties. Here you can lie back, put a mud pack on your face, relax and try not to let that whiff of sulphur put you off.

The Golden Circle: Þingvellir, Gullfoss and Geysir

The Golden Circle is a day tour of three of Iceland's natural wonders, only about 50 km from the city. Passing through the small town of Mosfellsbær you reach Þingvellir, seated firmly on the Mid-Atlantic Ridge which swoops diagonally through the country, northeast from the capital. At Þingvellir you can actually see the Eurasian and American continental plates draw apart from each other. From here you can get to Geysir, an area of spouting hot springs which gave its name to all such natural features the world over, and Gullfoss, a huge two-step waterfall that partially freezes in winter.

Akureyri, the Snæfellsnes Peninsula, Landmannlaugar and the Westman Isles

Beyond Reykjavík is a whole new world of lava fields, fjords and glaciers. Akureyri, the second largest city in the north of the country, is at the end of Iceland's longest fjord surrounded by a national park and provides the opportunity to reach the island of Grímsey on the Arctic Circle. The Snæfellsnes Peninsula, closer to Reykjavík, has an inspirational glacier, coastal walks and an impressive array of birdlife. Landmannalaugar in the central highlands is an area of outstanding beauty, with orange rhyolite mountains and a hot spring for outdoor bathing, as well as being the start point for one of Iceland's most spectacular hikes. Finally, the Westman Islands off the south coast have two volcanoes, walking trails and a host of puffin catchers in the summer months. The archipelago includes the island of Surtsey which emerged 40 years ago in a submarine volcano eruption.

The bohemian old town of Reykjavík is situated between two water features – the harbour and the pond. In between the two you'll find the centrepoint of the city, Austurvöllur Square, with the historic AlÞing parliament building and city cathedral, and some welcoming cafés on its borders. Follow the main street, Austurstræti, up the hill and it becomes Laugarvegur, the main shopping street. Above it on the hill is Hallgrímskirkja, a towering church designed to look like an erupting volcano – man, god and nature combined in almost frightening grandeur. Running quietly off Laugarvegur is Hverfisgata, a row of corrugated-iron houses in bright, primary colours with a lived-in appeal and wonderful views down to the water and beyond to Mount Esja. Down by the harbour you'll find the flea market at weekends with a fish hall at the back and, occasionally, fairground rides along the quayside, complete with children clutching those perennial favourites – candyfloss, pylsur and dried cod.

On the outskirts of the city you'll find two of Reykjavík's most idiosyncratic sights. Laugardalur Valley is the centre of Iceland's sporting activity and a bit of a hotspot. The name refers to the hot springs, now used to feed the city's biggest swimming pool, with steam room, Olympic-sized outdoor pool and a number of hot pots. Öskjuhlíð Hill has got the look of a secret military hideout built on the foundations of an old Second World War base, but the spherical Pearl building was not designed to be hidden, perched as it is like a broody hen, on top of six round tanks that store the city's hot water. It's the nearest thing the city has to the Eiffel Tower, with viewpoints out over the city and beyond, and a nice café inside. At the very top there's a revolving gourmet restaurant and a fabulous bar, but both are prohibitively expensive even by Icelandic standards. Down at the foot of the hill you'll find a yellow- sand beach, hot pots and a warmed-up section of the Atlantic that you can swim or paddle in.

On the Reykjanes Peninsula to the west of Reykjavík are two sights that make use of the natural surroundings. The dark, bumpy, moss-covered lava fields around Hafnarfjörður in particular have given rise to numerous stories about elves, pixies and angels, and a reputation for being home to the biggest otherworldly community in the country. And beyond it towards Keflavík is the world-famous Blue Lagoon, a steaming pool of opaque turquoise water that leaches minerals from the lava bed, filling it with healing properties. Here you can lie back, put a mud pack on your face, relax and try not to let that whiff of sulphur put you off.

Beyond Reykjavík is a whole new world of lava fields, fjords and glaciers. Akureyri, the second largest city in the north of the country, is at the end of Iceland's longest fjord surrounded by a national park and provides the opportunity to reach the island of Grímsey on the Arctic Circle. The Snæfellsnes Peninsula, closer to Reykjavík, has an inspirational glacier, coastal walks and an impressive array of birdlife. Landmannalaugar in the central highlands is an area of outstanding beauty, with orange rhyolite mountains and a hot spring for outdoor bathing, as well as being the start point for one of Iceland's most spectacular hikes. Finally, the Westman Islands off the south coast have two volcanoes, walking trails and a host of puffin catchers in the summer months. The archipelago includes the island of Surtsey which emerged 40 years ago in a submarine volcano eruption.