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Why go now?
Now that the equinox has passed, you get more daylight in Iceland than in Britain. And Reykjavik is set to become more accessible than ever with a flurry of new flights launching, beginning this week with easyJet's service from Luton. The weak local currency means relative bargains such as a pint of beer for only 700 kronur (£3.50). And once the temperature has risen, the city will stage the annual two-week Reykjavik Art Festival (artfest.is) starting on 18 May, a celebration of native and international music and dance.
As well as easyJet (0843 104 5000; easyjet.com), Icelandair (0844 811 1190; icelandair.co.uk) flies from Heathrow, Manchester and Glasgow. Iceland Express (0118 321 8384; icelandexpress.com) flies from Gatwick, with Stansted and Edinburgh commencing in June. Wow Air (00 354 590 3000; wowair.is) starts from Stansted in June.
International flights land at Keflavik airport, 48km west of Reykjavik. A taxi into the city will cost about ISK15,000 (£77). An airport bus shuttle offers a more cost-effective transfer. Flybus (00 354 580 5400; re.is/ flybus) meets all arrivals with a return ticket to the BSI bus terminal (1) costing ISK3,500 (£17). Journey time is about 50 minutes. For an extra ISK1,000 (£5) you'll be dropped off and picked up at your hotel.
Get your bearings
Ingolfur Arnarson came ashore from Norway in 872 and settled on a peninsula on the south-western corner of Iceland, naming it Reykjavik (meaning "Smoky Bay"). Located on the shores of Faxafloi Bay with Mount Esja (914m) and other peaks rising on the far side of the water, Reykjavik is easily explored on foot. The main sights, restaurants and shops are concentrated in the design district known as "101". Named after the postcode, it encompasses the streets around Laugavegur. The tourist information office (2) is at Adalstraeti 2 (00 354 590 1550; visitreykjavik.is; open at 9am daily, to 6pm Monday-Friday, 4pm Saturday and 2pm Sunday). A 48-hour Reykjavik Welcome Card for unlimited public transport and entry to most museums costs ISK3,300 (£17).
Hotel Borg (3) at 11 Posthusstraeti (00 354 551 1440; hotelborg.is) was the city's first luxury property when it opened in 1930. It still leads the way. Doubles start at ISK35,200 (£181), including breakfast.
Design lovers need look no further than Centerhotel Thingholt (4), well located at Thingholtsstraeti 3-5 (00 354 595 8530; centerhotels.com). Rooms are rugged yet hedonistic with bare concrete walls and leather floors. The decadent lobby bar features a wall made entirely from salmon scales. Doubles from ISK20,000 (£103), B&B.
It may, technically speaking, be a hostel but Kex (5) at Skulagata 28 (00 354 560 6161; kexhostel.is) has more style than some five-star hotels. Movie set designer Halfdan Petiersen has transformed this former biscuit factory on the waterfront into a stunning property inspired by Fifties America. Dorm beds from ISK2,200 (£11) and doubles with private bathroom from ISK11,800 (£61), room only.
Take a hike
Begin on the quiet shores of Lake Tjornin overlooking the modern City Hall (6), a building that divides opinion. Many locals think its industrial exterior is not in keeping with the area's heritage. This is the oldest part of the city, dating back to the 1760s. Walk along Tjarnargata before turning right on to Austurvollur, a leafy square and site for the world's oldest democracy: the understated Icelandic parliament building (7). Cross the square and travel north along Posthusstraeti before turning right on Tryggvagata, then left on to Laekjargata. You'll soon emerge on the waterfront facing futuristic Harpa concert hall (8), set against a mountainous backdrop. Then walk west along Geirsgata.
Lunch on the run
Stop at the indoor Kolaportid flea market (9) (00 354 562 5030; open 10am to 5pm weekends) to try Iceland's favourite snack: crisp-like pieces of dried fish. Or head for the collection of harbour wharf restaurants on Geirsgata, grab a stool and enjoy a steaming bowl of soup from locally caught lobster at Saegreifinn (10) (00 354 553 1500; saegreifinn.is) for ISK1,100 (£6). Open 11.30am to 10pm daily.
Big-name brands are noticeably absent from Reykjavik's main shopping street, Skolavordustigur (11). Hours are short: typically 10am to 4pm on Saturdays (to 6pm Mon-Fri, closed Sundays). Fashion boutique Nostrum at No 1a (nostrum.is; open from 11am) sells wares only from Icelandic designers. Minja at No 12 (00 354 578 6090; minja.is) is a trendy interiors store.
The National Museum (12) at Sudurgata 41 (00 354 530 2200; nationalmuseum.is; 10am to 5pm daily, closed Mondays between mid-Sept and the end of April; ISK1,200/£6) should be your first port of call. Detailing 1,200 years of history, it traces Iceland's journey from settlement to modern day.
Later, investigate the country's thriving art scene. Erro, famed for his collages and mosaics with political undertones, has a permanent exhibition at the Reykjavik Art Museum (13) (00 354 590 1200; artmuseum.is; open 10am to 5pm weekends, other days vary; ISK1,100/£5.50) – not to be confused with the Reykjavik Art Gallery (14) at Skulagata 30 (00 354 578 2060; reykjavikart gallery.is; 1-5pm weekends, 10am-6pm weekdays; free) which has abstract and figurative pieces by contemporary painters.
Islenski Barinn (15) at Posthusstraeti 9 (00 354 578 2020; islenskibarinn.is) sells more than 30 beers from micro-breweries across Iceland. Pints from ISK700 (£3.50). Alternatively, the darkened first-floor bar Boston (16) at Laugavegur 28b (00 354 517 7816), with gold-leaf wallpaper and mirrored pillars, is a nice spot to sip Brennivin – the potent national drink made from fermented potatoes and flavoured with cumin. Shots cost ISK800 (£4).
Dining with the locals
Tucked away in a residential street is Prir Frakkar (17) at Baldursgata 14 (00 354 552 3939; 3frakkar.com). The crammed tables are testament to the tasty food here. Dishes include smoked puffin breast in a mustard sauce and horse fillet with mushrooms. Mains from ISK3,500 (£18).
Less adventurous diners who are still keen to try local produce should opt for Einar Ben (18) at Veltusund 1 (00 354 511 5090; einarben.is). Go for the lamb loin with potato cakes for ISK5,100 (£26).
Sunday morning: go to church
Dominating the city skyline is the striking Hallgrimskirkja church (19) at the top of Skolavorouholt (00 354 510 1000; hallgrimskirkja.is), designed to resemble the basalt formations found across the country. Take a trip to the top of its 73m concrete bell tower (9am to 5pm daily; ISK500/£2) for views over the city's colourful rooftops.
The city's Domkirkjan cathedral (20) (00 354 520 9700; domkirk jan.is), next door to the Parliament building, is closed at weekends except for Sunday service at 11am. Don't let the fact that it's conducted in Icelandic put you off; pop along for a glimpse of its impressive altar painted by G T Wegener in 1847.
Out to brunch
The trendy Laundromat Café (21) at Austurstraeti 9 (00 354 587 7555; thelaundromatcafe.com), a Danish import, offers a dedicated brunch menu for saints and sinners, 10am to 4pm at weekends. Choose between the "clean" (including scrambled eggs, homemade hummus and fruit) or the "dirty" (spicy sausage, bacon and a rich local cheese) for ISK1,990 (£10). There are also fresh fruit juices, grilled sandwiches and the opportunity to wash your smalls in the laundrette downstairs.
A walk in the park
Reykjavik's best walking is Oskjuhlid, a forested hill just outside the city centre with the Pearl (22), a local landmark of six vast aluminium tanks and a glass dome, sitting at the crown. Gentle trails weave through pine woodland with views over the city and mountains from the top. Take a stroll down to Nautholsvik, a geothermal beach with sand imported from the western fjords.
Take a ride ...
... into the wild. Head out to sea to spot puffins (May-Aug) and humpback and orca whales on a wildlife cruise with Elding (00 354 555 3565; elding.is). Three-hour trips leave daily at 1pm from the harbour and cost ISK8,000 (£41).
Icing on the cake
At the Blue Lagoon, close to the airport (00 354 420 8800; bluelagoon.com; ISK4,800/£25), plumes of steam rise from the milky waters surrounded by hills of jagged and blackened lava.
But for a more local experience visit one of Reykjavik's 18 tourist-free city baths, all shown at swimminginiceland.com. Bjork's favourite is reputed to be Vesturbaejarlaug (23) (00 354 411 5150; 9am to 5pm Saturday, 11am to 7pm Sunday, weekdays vary) on Hofsvallagata, with a large outdoor pool and four bubbling hot tubs at 35-39C.