'Is this it?" says my son Tom incredulously as we drive into Akureyri. We pass a petrol station and a straggle of low-rise buildings and we are in the heart of Iceland's second city. The outskirts seem pretty cursory and then you realise the outskirts are the city. Akureyri (pop 16,000) is the Birmingham of Iceland. If this is the second biggest we try to imagine what Iceland's third city might look like. Half a dozen shacks in a field?
Akureyri sits at the southern end of Eyjafjordur Fjord, just 37 miles south of the Arctic Circle. With its single pedestrianised shopping street, handful of cafés and new edge-of-town mall, this "city" is the last word in urban sophistication locally. The town is also home to a golf course, a botanical garden and a university, stellar sights overlooked by tourists, who use the place to explore the north coast and nearby lake district of Myvatn.
The road along the eastern shore of the fjord shows Akureyri at its best: a low-rise skyline of neat white buildings with steep pitched roofs that are reflected neatly in the polished waters that curve around the town. The air is so clear it seems to sharpen the lines and saturate colours in a way that verges on hallucinatory. Above the town the hills rise gently and are capped with snow; in the fleeting sunshine of summer it all looks deceptively cosy. We try to imagine what it must be like in dark midwinter with Arctic gales blowing in from the unforgiving north. In our own little way we are about to find out.
The tiny fishing port of Husavik is 60 miles north-east. It comprises little more than a pointy headed Lutheran church flanked by a few houses with brightly coloured tin lids. They present a brave face to the Arctic Ocean but seem small and inadequate at this latitude. Husavik was settled first around 850 by a Swedish Viking called Gardar Svavarsson, but its most celebrated son de nos jours must be Eidur Gudjonsson, ex-Chelsea striker and one of only two famous Icelanders I can name. (More of the other one later.) As we wander down to the harbour a game of "spot the Eidur lookalike" produces enough to man a team.
Husavik is the whale-watching capital of Iceland. Tom and Niko (my sons) are the first of about 30 enthusiasts to board a squat and businesslike ex-fishing boat adapted to its new tourist mission. A brisk breeze has sprung up and the sun has vanished. An ominous mist has rolled in, decapitating the hills above the port. We are handed bright yellow oilskins and offered seasickness pills. With hindsight, these should have been warning enough.
My partner Julia is not a born sailor. She is in the hold rummaging for her camera when we clear the harbour wall and the first ocean wave hits the bow, throwing her off her feet and crashing to the floor. The boat is pitching and yawing wildly and it takes some effort to haul her up on deck. Everyone is drenched and at least half a dozen of the trippers are turning green. Julia, looking milky, sits on the rear deck with a hunted expression in her eyes. We are only five minutes into a three-hour ride around Skjalfandi Bay.
Tom is riding the bow, which must be lurching 25 feet vertically; it's a fairground thrill for him. I find my 10-year-old, Niko, inside his tent-like waterproofs hanging on to the deck rail with grim determination. He is quieter than normal but assures me he is fine. I hang on to him and wonder what the drill is for "child overboard".
We see puffins skimming the waves: the comedy support act in this wildlife show. About 45 minutes of stomach churning later, the PA shouts urgent instructions to look to port. We are rewarded with our first glimpse of the darkly arched back and dorsal fin of a minke whale. It does not last more than five seconds but there is jubilation on board.
Over the next two hours we find two more minke whales who are more generous with their face-time and on our way back we bag the biggie: a humpback. We can see and hear the column of spray being expelled from its blowhole, and follow the magnificent curve of its flukes as they clear the water before the animal dives. When it resurfaces we are close enough to count the barnacles clustered around the blowholes.
We return to port damp, chilled and thrilled to the marrow. One of the crew confides to me that they debated whether to sail in today's rough conditions. I am elated partially by the whales but also at having managed not to throw up. Julia has not been so lucky.
To restore our cold limbs we head south in search of the thermal springs at Lake Myvatn. Within minutes we leave the coastal landscape and quite possibly planet Earth behind. Nowhere else in Europe has such vast areas of unpeopled space. In this respect Iceland is both luxurious and unnerving. A vast lava field stretches in every direction; desolate and intimidating in its sheer otherworldliness.
Our "road" is marked only by yellow sticks that interrupt the lava periodically. The track leads in a straight line to the vanishing point where the grey brown streaked earth meets the sky. The flat horizon is broken by the cones of distant volcanoes. It's not just the kids who think it is entirely plausible that pterodactyls will swoop from the clouds.
As we near Lake Myvatn the Jurassic illusion is only fortified. This is ironic because the landscape is the result of disturbingly recent and ongoing volcanic activity. Calderas, barely solidified lava flows, sulphur striped mountains and lime green vegetation on the shore of the lake all add to the surrealism.
When we find the Myvatn Nature Baths the buildings seem prosaic structures that hardly do justice to the cinematic sweep of the location. Shivering against the late afternoon chill we emerge and gawp at 6,000 square yards of geothermal pool. The aquamarine water seems to be glowing; clouds of steam are billowing from the surface, rising into a low, menacing sky. Between the curtains of steam we can make out disembodied people, heads bobbing in the opaque mineral soup. The embrace of the superheated water as I lower myself in is instantly seductive. Julia finds it too hot and retires to the lobby where we find her looking bemused. She thinks she has seen a Björk lookalike. The Viking at reception is not a man of many words. I ask whether their national treasure has ever visited the spa. "Björk, you know, the singer?" I say. "Yes." "Has she ever been here?" "Yes." "Was she here today?" I press. "Yes," he deadpans. Apparently we have been bathing with Björk.
On the way back to Akureyri I find "Army of Me" on the iPod. Her fragile, plaintive voice fills the car. We pass between craters and jagged lava flows, the sky is descending and the horizon is receding.
"You're on your own now. We won't save you," sings the Icelandic elf.
HOW TO GET THERE
Sankha Guha travelled with ScanTours (020-7554 3530; scantours.co.uk). The seven-night Whales and Waterfalls trip takes in Akureyri and costs £820 per person, based on two people sharing, including return flights, b&b accommodation and car hire.