You're never too old for a facelift. After months of careful cleaning, Gothenburg's seven-metre-high (23ft) statue of Poseidon, now 81, looks better than it has in years. At first, residents hated the bronze figure which stands naked in a fountain at the top of the city's main boulevard. They said it was too big, and that its legs were too long for the body (a local myth says sculptor Carl Milles was asked to shrink the sea god's penis). But attitudes in Sweden's second city have come a long way since the 1930s, and right now there's an explosion of interest in all things cultural and challenging.
Start your cultural slice of the city at the towering yellow-brick façade of the art museum (00 46 313 683500; konstmuseum.goteborg.se; closed on Mondays), just behind the fountain. You'll see how far things have come. Rippling in the wind next to the tall, Neo-classical arches are banners advertising the next big exhibition: Andy Warhol and Francis Bacon (17 March to 12 August). Just a month or so ago, the gallery was showing off works by Mexican painters Frida Kahlo and Diego Rivera.
Further north-west on this street, Avenyn, is a nod to one of Gothenburg's famous exports (no, not the Volvo). The blackened metal statue of Karin Boye – whose dystopian novel Kallocain warns of a future where no secret is safe – stands solemnly outside the city library. It can be chilly enough here to freeze gloveless fingers, but out of either respect or pity (Boye killed herself in 1941) locals regularly take time to leave fresh flowers in her hand.
As you continue north-west past the tall, 19th-century townhouses, keep an eye out for Carl Fredrik Reuterswärd's 1980 Non Violence – an oversized sculpture of a revolver with a knot tied in its barrel.
Shoppers can make the far end of this street chaotic, so turn west on to Vasagatan, where the ivy-wrapped Röhsska Museet (00 46 313 683150; designmuseum.se; closed Mondays) uses wacky exhibits to shine a light on the Scandinavian obsession with form and function.
Beyond here, the buildings become ever more splendid, with Italianate balconies and glazed tiles lining their façades, until you reach Vasaplatsen, a road that slopes gently past a jumble of cafés and design emporiums.
Follow it and you'll soon emerge into Kungsparken, a leafy park that's dotted with granite sculptures. At its northern edge is the 17th-century moat that helped make Gothenburg one of the best-defended cities in Northern Europe. In the summer, tourists ply this skinny waterway on a boat tour known to locals as Paddan (The Toad), but in winter, when thick slabs of ice cling to the surface, you can't get anywhere fast.
The annual freeze must have made it difficult for the Swedish East India Company, founded here in 1731, to send its ships to China in search of tea and porcelain.
Keep going straight until you reach Norra Hamngatan and you can see the company's huge, copper-roofed headquarters, which has since been converted into the Gothenburg City Museum (00 46 313 683600; stads museum.goteborg.se; closed Mondays). Its gift shop (00 46 313 683610; closed Mondays) sells beautiful copies of old maps depicting how the world would have looked to the company's sailors in the 17th and 18th centuries.
Those days of exploration are over, but shipping is still central to Gothenburg's economy. Heading west of the museum and out along the riverside road called Skeppsbron, you'll see cranes soaring over the water like giant metal giraffes. Look closely among the graffiti-tagged containers and blocky Sixties apartment buildings, and you'll spot an old boat that's now being used as a floating multi-storey car park. It's ugly, but effective.
It doesn't take long to get back to the usual Swedish style. On Järntorget, 200 metres south of Skeppsbron's end, you'll find Svenssons i Lammhult (00 46 472 48700; svenssons.se), a shop full of beautifully minimalistic furniture that you never knew you wanted. But take care; prices here are more Harrods than Ikea.
Just around the corner on gritty Andra Långgatan, the retro Dirty Records shop (00 46 311 88483; cafe santodomingo.se) is a relaxed place to sip Dominican coffee while browsing through the stacks of old vinyl. Further along, past shop fronts daubed with vivid, cartoon-like street art in the shape of monsters, L'Assassino (00 46 311 41512; lassassino.com; closed Sundays) serves the biggest prawn sandwiches this side of heaven.
Double back on yourself down Tredje Långgatan for the final straight back to Avenyn. En route, you'll pass through the car-free streets of Haga, where cafés use candlelight and the sugary smell of cinnamon buns to lure in weary shoppers. If you can resist the urge to stop, continue along Vasagatan, and you'll soon be back near where you started, looking up towards Poseidon.
Gothenburg's newest crash pad is the Clarion Hotel Post (00 46 031 619000; clarion post.se), which was built in and around a vast 1920s post office building near the railway station.
To let your taste buds loose on some decent Swedish beers, many of which come from local microbreweries, check out ÖlstuganTullen (00 46 317 880989; olstugan.se), one of the newer bars on AndraLånggatan.
The new Juli&Jen shop at Kaserntorget 8 (00 46 703 815142; Saturday only from 11am-4pm) plays on Gothenburgers' love for all things vintage. Here, two ladies take used clothes and rework them into flashy new designs.
Gothenburg City Airport, the most convenient gateway, is served by Ryanair from Stansted and Edinburgh. The main airport, Landvetter, is served from Heathrow by British Airways and SAS (code-shared by BMI), and from Birmingham and Manchester by City Airline (code-shared by SAS).
First Hotel Avalon (00 46 317 510200; avalonhotel.se) has doubles from SKr 1,932 (£183).
WalkNet (00 46 704 567507; walknet.se) organises themed walking tours. Prices from SKr100 (£9.50) for a 90-minute tour.
Gothenburg Tourist Office: goteborg.com