Copenhagen (København in Danish) is the capital of Denmark and the city where I have lived most of my life.
Copenhagen is more than 1000 years old, and is today a lively and cultural modern capital where, if you are a tourist, you should spend at least several days to explore what the city has to offer.
As can be seen I have spent a considerable amount of time along the 3 lakes, which many tourists actually think is a river. They are mainly man made. In the old days they were part of the fortification of Copenhagen, but today they serve as a really nice recreational area.
The coast along North Zealand (Nord Sjælland in Danish) has for the last 100 years been the play ground for many (mostly rich) Danes from Copenhagen during the summer time. Gilleleje is one of the most well known places and it still is - as it was a 100 years ago - a small romantic fishing village well worth a visit.