Copenhagen is famous for its chocolate-box charm, typified by the Little Mermaid, cutesy cake shops, the Tivoli Gardens and a host of fairytale castles. But it also has many of Scandinavia's best designer cafés, bars, clubs and restaurants, a less seedy and more user-friendly version of Amsterdam. It also has some great modern art museums, tons of boutiques and, though discretion is advised, a liberal attitude to cannabis.

For the best of the new Copenhagen, ignore the city centre and head for the former working-class area of Nørrebro and the old red-light district of Vesterbro. This is where the action is. And further out in the suburbs, you can find the best contemporary sculpture and architecture as well as woodlands, sand dunes and fantastic beaches.

See the real sites

Police Museum - Fælledvej nr Skt Hans Torv, Nørrebro. Open Tues & Thurs 10am-4pm. Admission Dkr25. Eccentric, disturbing and entertaining museum set in Copenhagen's oldest police station. Displays of early illegal pornography, a wonderful Nimbus motorbike and photos of murder scenes - only look at these if you have a very strong stomach.

Arken - (arken.dk) S-train to Ishøj then bus 128 or 25-minute walk. Open Tues-Sun, 10am-5pm. Admission Dkr50. A spectacular art gallery built on a sand dune 10 miles from the city centre. You can combine beach, art and great architecture, although the exhibitions can be disappointing. Make sure you check out the fabulous toilets in the basement. A great café overlooks the sea.

Louisiana - (louisiana.dk). Local train to Humlebæk then 10-minute signposted walk. Open daily 10am-5pm, Wed closes at 10pm. Admission Dkr60. A breathtaking collection of sculpture and graphic art in a labyrinth of galleries overlooking the sound to Sweden. The outdoor children's area with giant Crow's nests and walkways is great fun.

Grundtvig's Church - S train to Emdrup then 10-minute walk. Open Mon-Sat 9am-4pm & Sun noon-1pm. Admission free. A strange organ-shaped church built in tribute to a founding father of the Danish state and a key figure in establishing the country's liberal traditions. Nearby are the large lakes and parks of Utterslev Mose.

Have a drink

Ungdoms Huset - Jagtvej 69 Nørrebro. A famous centre of radical politics. You'll still find the wilder youth subcultures here along with ad hoc people's cafés/bars, occasional jazz offerings and raucous concerts.

Pussy Galore's Flying Circus - Skt Hans Torv 30, Nørrebro. Check out the cocktails or the extensive schnapps list, then hang out on the square-side seating.

Bang & Jensen - Istedgade 130, Vesterbro. An ex-pharmacy with huge mahogany counter and high stucco ceilings. On Saturdays, it gets packed with students.

McKluud - Corner of Istedgade and Oehlenschlægersgade, Vesterbro. A rough and ready Danish pub in the heart of the red-light district. Can get a bit wild, but it's one of the few authentic drinking holes left in the area. Watch out for flying chairs.

Eat out

Salonen - Peblinge Dossering 6, Nørrebro. In summer, the lakeside terrace makes this one of the most genial spots in town. Decent coffee, ice cream, cakes and light meals. You can rent paddle boats

Oonas Kokken & Koktail - Engehave Plads 9, Vesterbro. Imaginative, tasty brunches from Hangoverhelper, which comes with a glass of cola and two paracetemol, to Trucker, a gut-busting burger with a bottle of Miller. Packed at weekends.

Sattva - Istedgade 98, Vesterbro. An organic bakery in the middle of the debauchery of Vesterbro, showing how much this area is changing. The cakes, bread and pastries are excellent.

Den Sorte Gryde - Istedgade 108, Vesterbro. The best takeaway burgers in the whole city.

Boyesen - Værnedamsvej 10, Vesterbro (+45 33317055). A chocolate shop, deli and affordable top-quality Danish eatery.

Restaurant Jacobsen - 449 Strandvejen (+45 39634322). Local or S train to Klampenborg and then five mins walk. A homage to Danish designer Arne Jacobsen situated in Bellavista, his famous white 1930s housing development. Fantastic food and a great location, make this one of the best eating spots around. Reserve a table in the evening and be prepared to pay for the experience.

Go clubbing

Vega - Enghavevej 40, Vesterbro (vega.dk). The hippest club in town. Rub shoulders, if you're lucky, with Bjork, Aqua and Helena Christiansen.

Rust - Guldbergsgade 8, Nørrebro (rust.dk). A nightclub-cum-bar, one of the best.

Go shopping

Starving Artistz - Elmegade 17, Nørrebro. Around 40 artists - amateurs,art students and some more established figures - sell their wares here. A bit hit-and-miss, though you should be able to find some bargains.

Storm - Men's Elmegade 13, women's Elmegade 4. One of the first boutiques to open in Nørrebro, in 1994. For designer clothes and accessories.

Don Ya Doll - Istedgade 55, Vesterbro. For strange moulded-rubber clubber wear. Worth a browse if you want to turn heads when you walk into your favourite night spot.

Konya Import - Istedgade 65, Vesterbro. A superb collection of plastic kitsch including religious figurines surrounded by flashing fairy lights.

Go to the beach

Bellevue - Local or S-train to Klampenborg station. A wonderful sandy beach backing on to an ancient forest.

Go to the funfair

Bakken - (bakken.dk) Local or S train to Klampenborg, then10-minute walk. Open April-Aug, noon-midnight. Admission free. Claimed to be the oldest amusement park in the world. A worthy alternative to stuffy Tivoli. Hot dog stands, ice cream stalls and some white-knuckle rides including a massive rickety old rollercoaster. Set in the huge and wonderful Dyrehaven Royal woodland.

Andrew Spooner is a contributor to the Rough Guide to Scandinavia and co-author of the Mini-Rough Guide to Copenhagen.

Way to go

Getting there: British Airways (0845 7733377) flies London Heathrow to Copenhagen from £99.99 return. Go (go-fly.com) flies London Stansted to Copenhagen from £55 return. Inghams Eurobreak (020-8780 7700, eurobreak.com) offers two-night weekend breaks to Copenhagen from £209pp including flights and B&B accommodation. Travelscene (020-84249648, travelscene.co.uk) offers two nights' B&B from £242pp including flights.

Where to stay: DGI Byen (+45 33298050, dgi-byen.dk) Tietgensgade 65, Vesterbro. From Dkr925 a night. A sleek example of Danish design with fantastic rooms all with internet connection. The swimming pool/spa offers a sauna and therapeutic massage.

Getting around: Like the Dutch, the Danes love cyclists, and when the sun is out excellent bike paths make cycling the best way to get around. Either try the solid-wheeled city bike - only to be used in the city centre - for a refundable Dkr20, or rent from the Cykelcenter, next to the central station, at Reventlowsgade 11 for Dkr50 per day. The suburbs are easily reached by public transport.

Futher information: Danish Tourist Board, (020-7259 5959, dtb.dt.dk). Flight time from London: 1h 50m. Time difference: +1 hour. £1 = Dkr11.92. Country code: 00 45