Reykjavík may seem like a mystifying place, but this two-day itinerary will have you feeling like a hearty local.

Day one:

Early risers should visit the bustling working harbour to watch the fishing boats come in. It's backed by stunning views of the peak Esja, across the fjord in southwest Iceland. Afterwards, head for breakfast at Grái Kötturinn, a tiny eccentric cafe serving bacon, eggs and hunks of fresh bread.

Next, meander up arty Skólavörðustígur, poking your nose into its crafty little galleries. At the top of the hill is the immense concrete church Hallgrímskirkja, Reykjavík's most dramatic building. For a perfect view of the city, take an elevator trip up the tower. Once you've plumped back down to earth, pop across the road to the Einar Jónsson Museum. You'll get a free glimpse of this gloomy sculptor's weird works in the garden round the back; if you like what you see, there are plenty more fantastical sculptures inside.

For further research into the Icelandic mind, head to the National Gallery of Iceland. Here, paintings by the country's most treasured artists include hallucinogenic landscapes and eerie depictions of folk-tale monsters. Pop into cosy Café Paris for a light lunch – it's a prime people-watching spot. Then, if you're here at the weekend, make Kolaportið your next stop – rummaging through foreign flea markets is always enlightening! You can also buy cubes of infamous hákarl (rotten shark meat) from the fish market – it might look innocuous, but find a quiet bin to stand by…

Next, catch bus 18 from Lækjartorg bus station to Perlan. There are two excitements here: first is the superb Saga Museum, which brings Iceland's early history to life with fantastically realistic models and a soundtrack of horrible screams – we think the Vikings would approve. Second is the hexagonal viewing deck and cafe, where you'll get tremendous views. For dinner,make sure you've booked a table at one of the capital's excellent seafood restaurants, such as Við Tjörnina. Once the bill's been settled, head back to your hotel for a kip and a freshen-up: you're going to need some energy to get you through the runtur, Reykjavík's notorious Bacchanalian pub crawl, which starts around midnight and carries on until 5am. Rather than cosying down in one venue, it's the done thing to cruise from bar to bar. To get you started, try perennial favourites Kaffibarinn, Kaffi Sólon) and Thorvaldsen Bar.

Day two:

After the night you've just had, start the recovery slowly with brunch at Café Oliver. At 12.30pm we recommend taking the 'express' version of the Golden Circle tour. OK, so it's a bit of a rush – maybe next time you'll book more than two days in lovely Iceland! At least you get to see some of the Icelandic countryside and marvel over two of its natural wonders – the tumbling waterfall Gullfoss and the spouting hot springs at Geysir.

Tired but happy, you'll get back to Reykjavík in the early evening just in time for dinner. For a dash of spice, why not try an Indian meal made with Icelandic ingredients? Go for succulent tandoori salmon at Austur Indía Félagið, or try the unique guillemot dish at Indian Mango. Round off the evening at the Volcano Show, an explosive introduction to Iceland's violent geography.

'What about the Blue Lagoon?' we hear you ask. Well, here's the clever part – you can visit Iceland's number-one attraction on your way back to the airport tomorrow. Wallowing in its warm, sapphire-blue waters is certainly a fantastic last memory to take home.

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