Vesterbro is a dynamic, youthful neighbourhood well worth a visit. Istedgade is the main street to wander down. By the central station there are sex shops, tourist hotels and a mini Chinatown, but continue on and soon lively middle-eastern green grocers, trendy boutiques and wonderful cafes appear.
A high concentration of great and varied restaurants, fantastic coffee places and an invaluable insight into the daily life of Copenhageners are to be found in this old working class neighbourhood.
To the left of the Central Station on the map. Walk up Istedgade to Enghave Plads (square). At an amble it'll take a relaxing 30 minutes.
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The development is not all bad, however. The streets are safer and there is still a good vibe in many places. Visitors interested in a long-ish walk could take a stroll down Istedgade from central station to the Enghave Plads square, then hang a sharp left and head up Dybbølsgade to Dybbølsbro S train station and the Fisketorv shopping centre.
From here it is possible to cross the water on the new pedestrian bridge, and stroll along the former harbour front at Amager before crossing back into the city centre via the Langebro Bridge. About 4 or 5 km in total.