Aside from several excellent museums, including the famous Nationalmuseet (National Museum), which has an excellent collection of exhibits celebrating Danish history and culture throughout the ages, Copenhagen is also home to a vibrant nightlife around the city, where you can let your hair down in clubs, and enjoy Danish cuisine in some high quality restaurants.
Sitting proudly in the centre of the harbour, you will see the statue of the little mermaid celebrating the life of Hans Christian Anderson. The statue has become a symbol of the city, although has fallen victim to several traumatic experiences over the years including a recent decapitation, and being dressed in a bra and knickers by a prankster.
Tivoli Gardens have a theme park with lots of rides and cater for families. During the week is the best time to visit, as the queues are minimal because all the locals are at work. The gardens are also a popular meeting place in the summer, and nearby is the Stroget area, where you can find a shoppers paradise centred on the largest pedestrian mall in Europe.