Not to miss

Ilulissat

Ilulissat translates as 'the icebergs', an entirely fitting name for a town that gazes out on a mirrored sea crammed with icebergs and floes. Ilulissat still has a frontier feel; its scruffy, feisty spirit at odds with its status as one of Greenland's most popular tourist destinations.

The man who is famous for, among other things, uttering the words, 'Give me winter, give me dogs, and you can have the rest,' has a museum - the Knud Rasmussen Museum - named in his honour. Inside are exhibitions dealing with his Arctic expeditions, as well as Danish and Inuit artefacts.

One of the major attractions is the Ilulissat Icefjord. The face of the Sermeq Kujalleq glacier measures 5km (3m) wide and umpteen metres thick; it's the world's most prolific glacier outside Antarctica and a source of one tenth of the glaciers swanning around Greenlandic waters.

Hiking tracks are marked with blazed cairns, although the easiest and most pleasant hike is the one that takes you to the ruins at Sermermiut and Holms Bakke, where the entire town of Ilulissat gathers to welcome the sun back on 13 January. Other hikes include the five-hour circuit to Vandsøen and back, and the more challenging trip to Akinnaq and back.

Nuuk

Nuuk (formerly Godthab) is Greenland's capital but not one of its tourist attractions. Kolonihavnen, the small old-town area, makes a pleasant exception to Nuuk's somewhat harsh, apartment-dense, Lego-city look.

If the Nuuk is the only stop you make in Greenland you'll find it quaint, if somewhat rainy, with some fine day hikes and fjordland boat rides nearby. While the city is small by modern standards, with a wealth of land and a paucity of people, most of the population are housed in immense apartment blocks and the urban sprawl is now spreading out along the road to the airport.

Nuuk was founded by the unfailingly optimistic Hans Egede - the Danish missionary with soul-conversions on his mind - who named the settlement Good Hope (Godthåb). The naming turned out to be more of a Hail Mary than a prophecy: first the native Inuit moved out of a neighbourhood that, to their way of thinking, had become too congested, and later smallpox and tuberculosis epidemics ripped through the settlement.

Ilulissat Kangerlua

The greatest tourist attraction in all of Greenland is the astonishing Ilulissat Kangerlua (Ilulissat Icefjord), a berg-packed bay fed by the 5km (3mi) wide and 1100m (3608ft) thick glacier Sermeq Kujalleq. The glacier flows an average of 25m (82ft) daily and is the world's most prolific outside Antarctica.

A Unesco World Heritage site since 2004, the bay's mouth is filled with bergs the size of apartment blocks or whole towns. There's no sight more mesmerising than gazing upon these monsters and listening to the almighty thunderclap roars that they emit when they fissure or explode in the warmth of the summer sun. Best of all the whole spectacle can be seen without the expense and organisation of a boat or helicopter rental that you'll need to see other ice-fjords around Greenland. From November to April Ilulissat is also a possible base for organising dog-sled tours.

The Southern Fjords

Astonishingly grand spires of granite soar straight out of Greenland's southernmost fjords like the teeth of an interplanetary crocodile. Climbers rate the rock faces of peaks like Uiluit Qaaqa (Ketil), Ulamertorsuaq (Uli) and The Baroness as among the world's finest challenges.

For the less active it's easy to put your head right in the crocodile's mouth by simply cruising down one of the fjords.

Most visits start from Nanortalik, itself a truly delightful village whose entire old town area has been preserved as a heart-burstingly picturesque living museum. The main choice is between Tasermiut, a truly grand fjord leading to a nose of glacier, or the shorter but arguably more spectacular Torssuqatoq which culminates with the extraordinarily photogenic village of Aappilattoq. With more time and patience there are yet more fabulous fjords to discover beyond Aappilattoq, though there's always a danger that all access is blocked by pesky floating ice-floes.

Although public ferries go down some lovely fjords from Nanortalik, the very finest require boat-hires, tours or hitching a ride with local hunters

Kulusuk

In many ways Kulusuk is an unlikely focal point for travellers; it's a small island, a mere dot, off the east coast of Greenland. In other ways it's the perfect place for a rendezvous with Greenland. Its international airport makes it easily accessible by air and frequent flights from Reykjavík make it ideal for day trips.

Kulusuk is the perfect introduction to Greenland; the tiny village clings to the rocky island above a glittering sea of icebergs with dramatic mountain peaks as a backdrop. Many of the residents still survive by hunting. Curiously enough, Kulusuk remains relatively immune to Western influence despite the regular influx of tourists, partly because the villagers follow a more traditional way of life and partly because visitors tend to only stay short-term.

Don't miss the beautiful, haunting cemetery, which is festooned with plastic flowers and set against a stark and icy Arctic landscape. Icelandair organises informal qajaq demonstrations and dance performances, but all bets are off if the performers prefer to go hunting.

The island is relatively small so hiking from the airport to the village won't take more than 40 minutes. The walk takes youu across the Arctic tundra carpeted in Arctic flowers and glacier buttercups, or you can hike straight up the hill to an eerie moutnian lake before descending to the town.