Stockholm

Gamla Stan, set on its own island at the city's heart, is one of Europe's best-preserved medieval town centres and the obvious place to begin. Its tight grid of cobbled lanes — including Mårten Trotzigs gränd, the city's narrowest alley — winds between tall, colourful gabled merchant houses to the broad square of Stortorget, ringed by photogenic façades and home to the Nobel Prize Museum. The huge baroque Royal Palace, one of the largest in the world still in use, holds state apartments, the treasury and a daily changing of the guard. The Storkyrkan cathedral, the German Church's spire, antiquarian shops, cellar restaurants and cosy cafés fill the lanes, and the waterfront quays around the island give classic views across to the City Hall and Södermalm. It is touristy but genuinely beautiful, and magical in the evening once the day-trippers leave.

The green island of Djurgården, a short walk, tram or ferry from the centre, concentrates Stockholm's best museums in a parkland setting. The unmissable Vasa Museum is built around the Vasa, a colossal royal warship that capsized and sank in the harbour on its maiden voyage in 1628 and was salvaged, astonishingly intact, in 1961 — to stand here, ten storeys of carved oak hull preserved before you, is one of Europe's great museum experiences. Beside it, Skansen is the world's oldest open-air museum, gathering historic timber buildings from across Sweden along with a zoo of Nordic wildlife (bears, wolves, moose) and seasonal festivals. The ABBA Museum celebrates Sweden's pop legends interactively, the Nordic Museum tells the country's cultural story in a palatial building, and the amusement park of Gröna Lund and the waterfront walks make Djurgården a full and varied day out.

Beyond the Old Town and museums, Stockholm rewards wandering. The City Hall (Stadshuset), a national landmark on the Kungsholmen waterfront, is where the Nobel Prize banquet is held each December beneath its golden Hall; its tower can be climbed for the finest panorama of the city's islands. South across the water, Södermalm (“Söder”) is the city's hip, hilly island — vintage and independent shops, the design boutiques of the SoFo quarter, the photography museum Fotografiska on its waterfront, and clifftop viewpoints like Monteliusvägen and Fjällgatan looking back over the Old Town and the harbour. Swedish design and fashion fill the shops of the central Norrmalm and Östermalm districts and the food halls like Östermalms Saluhall, while fika — the daily ritual of coffee and a cinnamon or cardamom bun, and a fixture of Swedish food — gives an excuse to pause in the city's many cafés. Even riding the metro (Tunnelbana) is sightseeing: many of its stations are painted and sculpted into a celebrated underground art gallery.

Stockholm's greatest escape is the archipelago — a scatter of some 30,000 islands, skerries and islets fanning out into the Baltic, from wooded, summer-house-dotted isles close to the city to bare, windswept rocks at its outer edge. In summer a fleet of white archipelago ferries, which function as genuine everyday public transport as much as tourist excursions, and form part of Sweden's wider transport network, makes day trips and island-hopping easy: Vaxholm with its fortress, the artists' island of Sandhamn, the rural calm of Grinda or Utö for swimming, cycling and fresh seafood. Even a short hop delivers the quintessential Swedish summer of red cabins, jetties and clear water. On the lake side of the city, a boat trip up Lake Mälaren reaches Drottningholm Palace, a UNESCO World Heritage Site and the royal family's residence, with its baroque gardens, 18th-century theatre and Chinese pavilion. Between the medieval old town, the island museums and the open water, Stockholm offers a rare combination of city culture and accessible nature.