Iceland has the scenery covered – geysers, black sand, cascading waterfalls. But a growing number of travellers are discovering that Reykjavik, a capital of just 140,000 people, also punches far above its weight artistically. The country holds a Guinness World Record for the most writers per capita, and one in ten Icelanders is said to publish a book. It starts with the airport taxi: the writer's driver, a musician and songwriter on the side, shrugs that this is completely normal in a country whose literary roots go back to the 12th-century sagas.

Music is the city's other calling card. Harpa Concert Hall, a honeycomb glass building on the waterfront modelled on Iceland's volcanic geology, anchors the calendar with Iceland Airwaves each November. On a recent visit, audiences caught Hildur Guðnadóttir – the Oscar-winning cellist behind the Tar and Joker soundtracks – playing her brooding, cinematic sets in the hall's dramatic red-and-black auditorium. Downstairs, Hnoss Bistro serves ling fish in cream sauce with views over Faxaflói Bay.

The experimental streak doesn't stop there. Fischersund, down a cobbled alley, is a family-run parfumerie and art collective whose handmade Nordic botanical scents double as stage sets – during the Reykjavik Arts Festival, 800 people swayed in dry ice to ambient electronics while notes of moss, grass and birch filled the air. There's also a speakeasy called Amma Don (Icelandic for grandmother), entered by pressing a brass lion knocker and decorated like a kitschy 1960s sitting room, pouring reimagined negronis with brown butter and rye. Björk's influence is everywhere: the National Gallery of Iceland recently hosted her immersive three-room video installation "Echolalia" alongside more than 80 masks by her long-time collaborator James Merry.

Even culture junkies need a reset. Ninety minutes from the city, Gullfoss plunges into a 70-metre canyon as one of Europe's most powerful waterfalls – a classic day trip. Quieter is Laugaras Lagoon, a geothermal spa that opened last December, where the Ylja restaurant serves a five-course tasting menu (fermented tomato carpaccio, Arctic char with horseradish, lamb in soy, basil granita) for £77 – reasonable by Icelandic standards – before you float in steaming pools or swim under the waterfall linking the two lagoons.

Practically speaking, Icelandair flies from London Heathrow to Reykjavik from around £200 return, and Alda Hotel, a modern boutique spot on the main shopping street Laugavegur, has rooms from £146 a night with a hot tub, sauna and Nordic buffet breakfasts. One quirk to plan around: summer sunsets are absurdly late, so streets stay lively well past 11pm and the night is only getting started.

For travellers who want the Iceland photo stops and an actual urban holiday – festivals, galleries, ambitious restaurants, proper nightlife – Reykjavik delivers both without choosing between creativity and calm.