Perhaps it’s the geothermal spa pools or the geographic isolation that make Iceland’s pocket-sized capital so laid-back.

What to see & do in Reykjavík

Warm to Reykjavík in a steaming, naturally heated geothermal pool. Laugar is the classic  www.laugarspa.is; entry £2.30. It might feel slightly Eastern Bloc – retinal-scan entry suggests you won’t be let out until you’ve won an Olympic medal – but it has six types of sauna, hot-stone massages and hot tubs where you can relax as diaphanous steam curls around you.

Laugar geothermal pools

Get your bearings on a bike tour (00 354 694 8956, www.icelandbike.com; £22) and your guide might take you to see Sólfar (Sun Voyager), Jón Gunnar Arnason’s Viking-vessel sculpture ; the home of the world’s first democratically elected female president; a hot-dog stand visited by Bill Clinton; and Björk’s house.

Viking Ship Sculpture Reykjavik

Above is a sculpture, Sólfar, inspired by Viking ships on the Embankment in Reykjavík

On Viðey island , reached by ferry from Sundahöfn harbour  www.elding.is; £5.40, Yoko Ono’s tribute to John Lennon, the Imagine Peace Tower, fires a white beam into the night sky from October 9 to December 8. ‘No pollution, no war,’ was her reason for choosing Viðey, which translates into perfect tranquillity. Catch the last boat back for delicate watercolour sunsets.

Sunday-morning hangover? Time for caffeine. There’s not much of a ‘coffee to go’ culture in Reykjavík’s myriad cafes – regulars sit for hours amid the scent of roasting beans. Revived, stroll around Tjörnin lake, where Lego-coloured houses are reflected in glassy water, broken by swan wakes. Pop into City Hall (Tjarnargata 11) to admire a topographic map of Iceland and the tenacity of those who civilised its inhospitable contours.

Einar Jónsson, Iceland’s premier sculptor, chiselled out hard-hitting political allegories at the turn of the 20th century. There’s more bas-relief than light relief at his museum www.lej.is; £3.25, but things are a bit more chilled in the garden, where 26 monumental bronzes have room to breathe, and a sensual patina when it rains.

Across the road, the stern, soaring exterior of Hallgrímskirkja church, www.hallgrimskirkja.is; tower £2.50 has a touch of Gotham about it. Meditate amid the more soothing Lutheran simplicity inside, while church bells ring the hours in crystal tones. A lift takes you up to the bell tower for the city patchwork below, and mountain views beyond.

Say thank you for the music at the Harpa cultural centre www.harpa.is. Economic meltdown meant it almost didn’t open last August, but it’s now a welcome, if incongruous, harbourside sight. Iridescent glass bricks glitter like fish scales, while the wilderness’s chalky cold colours stretch out behind. Inside, three concert halls host Icelandic and international artists.

Enjoy the best show in town from September to April, as gaseous particles collide with the Earth’s atmosphere, dancing across the night sky like lime-coloured chiffon. Minimal light pollution in the city means it’s possible to see the Northern Lights while walking home from the bar. Or take a 4WD  www.superjeep.is; from £92pp out into icy moonscape scenery for the widescreen experience.

Where to eat

Saegreifinn (Geirsgata 8; 00 354 553 1500, www.saegreifinn.is). You know it’s good if local fishermen come – and this shack does the best lobster stew. Warm up with a mug, and the tang of seaweed in your nose, at a canteen-style outside table. Inside, buoys serve as seats, while fishing nets and wonky pictures add ‘front room’ charm. Mains around £5.

Hamborgara Búllan (Geirsgötu 1; 00 354 511 1888, www.bullan.is). This Icelandic take on Americana feels curiously authentic, albeit in a 1950s time-warp way. With a scattering of high tables and pictures of a young Frank Sinatra, this modest corner diner is elevated by rocking burgers. Mains around £5.

Forréttabarinn (Nýlendugata 14; 00 354 517 1800, www.forrettabarinn.is). Boquerones and bravas? That’s old tapas hat. Try the Icelandic take on Spanish grazing, with chichi plates of lamb’s heart with dates, fried salted cod and arctic char with juniper berries and sweet bourbon. Tapas dishes £5 each.

Fish Market (Aöalstræti 12; 00 354 578 8877, www.fiskmarkadurinn.is). There’s a darkroom vibe to the orange-lit wood interior – use your other senses to enjoy salted cod spiced with lime zest, served with cranberries and Jerusalem artichoke, along with other mash-ups of local produce. Mains around £20.

Grill Market (Lækjargata 2a; 00 354 571 7777, www.grillmarkadurinn.is). The city’s trendiest restaurant borrows its fairy dust from the designer Tom Dixon – his metal filigree droplight hogs the stairwell. Downstairs in this old cinema, there’s moss on walls and catfish-skin screens, lit from behind. Book ahead and try the lamb fillet fed on angelica. Mains around £25.

Dill Restaurant (Sturlugötu 5; 00 354 552 1522, www.dillrestaurant.is). The aim here? To put Scandi-style food up with the French and Italian big boys. The sommelier, Olafur Orn Olafsson, pairs well-chosen wines and modern seasonal Nordic food – try scallops, sea buckthorn and pine needles – with Michelin-dainty presentation. Three-course menu around £40, excluding wine.

Where to shop

Handknitting Association of Iceland (Skólavördustígur 19; www.handknit.is). No longer the preserve of Perry Como, the patterned sweater, or lopapeysa, reaches new levels of cool in Iceland. They are fabulously soft, thanks to wool from long-haired sheep. Buy off-the-peg at this knitting collective – or go DIY with patterns and yarn.

Kron Kron (Laugavegi 63B). Icelandic Betty Boops shop for colourful leather and suede heels with buckles and bows. The shoes are fairy-tale creations, the prices less whimsical – around £295 a pair. At least nobody will have them back home.

Nightlife
Kaffibarinn (Bergstaoarstraeti 1). Reykjavík’s Noughties church of partying (it’s part-owned by Damon Albarn) is a candlelit place to chase down Reyka (Icelandic vodka) with an Opal (Nordic sambuca), until 5am at weekends.

Lebowski Bar (Laugavegur 20a). Styled around cinema’s The Big Lebowski, this quirky new bar might not have a bowling alley, but it makes up for it with potent White Russians and a rammed dancefloor at the weekends.

Silfur (Hotel Borg, as before). Hub of Icelandic glamour, this Art Deco den has a mirrored bar, an open fire and burnt and lacquered Maarten Baas ‘Smoke Chairs’. Ignore the naff volcano video and drink potent Apple Martinis.

Ask the local

Designer Aaron has lived in Reykjavík for nine years

‘Buses are frequent, clean and go almost everywhere, but Reykjavík is small, so you can get to most places on foot. Explore the regenerated area around Myrargata , with its creative workshops and coffee shops. Order the latest trendy brew – Icelanders often win barista championships – but don’t overlook the verkamannakaffi, or ‘worker’s coffee’. It’s basic, but with endless refills, and better than any coffee I’ve had in England. Don’t go anywhere that looks like a Tex-Mex place; tourist food is always awful. But do go to restaurants where you can’t read the Icelandic menu. This way, you’re likely to eat something good, such as meat soup. Buy a traditional ‘lopi‘ sweater, but one from the Red Cross shop on Laugavegur . It will have that aged look that makes you feel invincible when you wear it.’

Further information
For more details on the city, check out the Visit Iceland website (www.visiticeland.com) and Visit Reykjavík (www.visitreykjavik.is).