With canals, historic buildings and cutting-edge architecture, the Danish capital is stunning at any time of year – but it is at its festive best right now. By Aoife O'Riordain

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Travel essentials

Why go now?

Copenhagen's stint as host for the United Nations Climate Change Conference has come to an end, which means the Danish capital can get back to doing what it does best: looking festive in the run-up to Christmas. The city is imbued with as much magic as a Hans Christian Andersen fairy tale, with several festive markets under way, notably at the Tivoli Gardens (1), and present-buying opportunities galore in its stylish design shops.

Touch down

I flew with SAS (0906 294 2772; flysas.com), which flies from Aberdeen, Birmingham, Heathrow, London City and Manchester. British Airways (0844 493 0787; ba.com) flies from Heathrow; easyJet (0905 821 0905; easyjet.com) from Gatwick, Manchester and Stansted; BMI (0870 60 70 555; flybmi.com) from Birmingham and Glasgow; Norwegian (020-8099 7254; norwegian. com) flies from Edinburgh and Gatwick; and Cimber Sterling (00 45 70 10 12 18; cimber.com) from Edinburgh, Gatwick and Newcastle.

Copenhagen's sleek Kastrup airport lies 8km to the south of the city; the connecting rail service takes 13 minutes to reach the city's central station (2) and costs 31.50 Danish kroner (£3.80) one way. Taxis cost around DKr250 (£30).

Get your bearings

Sitting on the eastern edge of Sjaelland, Denmark's largest island, Copenhagen is an enchanting mosaic of canals, historic buildings and cutting-edge architecture. The medieval heart of the city is bordered by neighbourhoods including up-and-coming Vesterbro, leafy Frederiksberg, cosmopolitan Norrebro and the bohemian enclave of Christianshavn. Most of the city is easily tackled on foot, but its efficient public transport system is also useful. Pick up a map at the Copenhagen Right Now centre (3), Vesterbrogade 4A (00 45 70 22 24 42; visitcopenhagen.com), close to the Tivoli Gardens (1) and the train station.

Check in

The Moorish Hotel Nimb (4), Bernstorffsgade 5 (00 45 8870 0000; nimb. dk), has 13 smart rooms and views of the Tivoli Gardens (1). It is the most exclusive place to lay your head in the city and the prices reflect this; doubles start at DKr2,500 (£305), room only.

The well-placed Hotel Twentyseven (5), Longangstraede 27 (00 45 7027 5627; hotel27.dk), has a young, buzzing atmosphere and rooms with functional décor from DKr1,113 (£134), including breakfast.

Wakeup Copenhagen (6), Carsten Niebuhrs Gade II (00 45 448 00010; wakeupcopenhagen.com), opened in September, and its status as the city's best budget option belies its distinguished architectural pedigree: it was designed by the son of Jorn Utzon, the Danish architect responsible for the Sydney Opera House. Doubles start at DKr400 (£48), room only.

Day one

Take a hike

Start at the regal splendour of the winter residence of Queen Margrethe II, the Rococo Amalienborg Palace (7) – actually four buildings arranged in a circle. Walk towards the quayside and gaze across the water at the spectacular Opera House (8) designed by revered Danish architect, Henning Larsen. Turn right and continue along the waterfront until you reach another of Copenhagen's contemporary showpieces, the glassy Royal Danish Playhouse (9). Bear right down pretty Nyhavn, with its gabled houses and boat-cluttered harbour, cross the bridge and turn left passing along the water's edge. Turn right along Havnegade until you reach Knippelsbro Bridge (10). Once you have reached the other side turn around and admire the view of the Royal Library (11), otherwise known as the Black Diamond. Afterwards, lose yourself in the pretty cobblestone and canal-lined streets of Christianshavn – the city's charming boho neighbourhood.

Take a view

There are far-reaching rooftop views from the top of Round Tower (12), Kobmagergade 52 (00 45 33 730 373; rundetaarn.dk). Built in 1642 by order of King Christian IV, its 209 metre-long internal spiral ramp enabled him to ride his horse to the top. It opens daily from 10am-5pm. Admission DKr25 (£3).

Lunch on the run

Polser or hotdog stands are ubiquitous all over the city and everyone has their favourite spot. Nyhavns Polser on Nyhavn (13), sells extremely tasty examples for DKr25 (£3).

Window shopping

Stroget is Copenhagen's main shopping thoroughfare, actually a collection of several different streets stretching from Torv Nytorv to Ostergade to Kongens Nytorv (as you approach the latter the shops get ritzier). Danish design is well regarded the world over and there is nowhere better to discover it than at Illums Bolighus (14), 10 Amagertorv (00 45 33 14 19 41; illumsbolighus.com), a paean to all things stylishly Scandinavian. Be warned, though: many shops shut by 5pm or 6pm on Saturdays and are closed on Sundays.

Cultural afternoon

Spend a few enlightening hours learning the history of Denmark from the Iron Age to the present day by way of the informative exhibits at The National Museum of Denmark (15), Ny Vestergade 10 (00 45 33 13 44 11; natmus.dk). Open 10am-5pm daily except Monday, admission free.

The profits of the Carlsberg beer empire are responsible for the enviable collection assembled by brewing magnate Carl Jacobsen at the Ny Carlsberg Glyptotek (16), Dantes Plads 7 (00 45 33 41 81 41; glyptoteket.com). Everything from Roman statues to Impressionist works by Degas, Monet and van Gogh are inside this impressive building, which also contains a charming winter garden and a wonderful extension by Henning Larsen. Open 11am-5pm daily except Monday. Admission DKr60 (£7.30).

An aperitif

Expertly mixed cocktails and a lively atmosphere are just two reasons to start a night on the town at Bar Rouge in the Hotel Sankt Petri (17), Krystalgade 22 (00 45 33 45 91 00; hotel sktpetri.com).

Dine with the locals

The meatpacking district of Vesterbro is currently the coolest part of Copenhagen. Here the smart set head for Kodbyens Fiskebar (18), Flaesketorvet 100 (18) (00 45 32 15 56 56; fiskebaren.dk), with its mesmerising centrepiece of a cylindrical jellyfish tank. Book in advance or queue for a place at its central zinc topped bar. Expect to pay DKr500 (£60) per person.

Take a ride

Climate Change Conference or not, there are few places more bike friendly than Copenhagen, with 300km of cycle paths to get around on. The free City Bikes (bycyklen.dk) scheme runs from April to November. However, outside these months you can rent a cycle from Baisikeli (19), Turesensgade 10 (00 45 26 70 0229; cph-bike-rental.dk), which uses its profits to send second-hand bicycles to Africa. Six hours' rental costs DKr50 (£6).

Day two

Sunday morning: go to church

The gilded helter-skelter-like campanile of Vor Frelsers Church (20), Sankt Anne Gade 29 (00 45 32 54 68 83; vorfrelserskirke.dk) is one of Christianshavn's most identifiable landmarks. Built in the 1680s, this church, with its impressive carved organ supported by two elephants, is one of the few examples of Baroque architecture in the city. Morning mass takes place at 10.30am.

Out to brunch

If you want to mingle with Copenhagen's beau monde, the ever-busy Café Victor (21), Ny Ostergade 8 (00 45 33 13 36 13; cafevictor.dk) is the best place to go. This brasserie-style restaurant serving Danish-meets-French cuisine offers brunch from 9am to 3pm at weekends for DKr175 (£21).

A walk in the park

For all its kitsch, The Tivoli Gardens (1), Vesterbrogade 3 (00 45 33 151 001; tivoli.dk) have a special place in the heart of most Danes and are at their best in the run-up to Christmas. Between now and 30 December they simply shimmer with Yuletide cheer thanks to a Christmas market and thousands of twinkling fair lights. Open 11am-10pm daily (Fridays and Saturdays to 11pm), admission DKr95 (£11.50) for adults.

The icing on the cake

Go and pay your respects to arguably one of the greatest architects of the 20th century with a visit to the Arne Jacobsen- designed Radisson SAS Royal Hotel (22), Hammerichsgade 1 (00 45 33 42 60 00; radissonblu.com), which celebrates its 50th anniversary in 2010. Ask nicely and the concierge might even let you sneak a peek at the unaltered top floor Alberto K restaurant that still sports the original Jacobsen- designed swan chairs and cutlery – all set off by some fabulous views of the city.