We have mainly visited (and I advise) :

 - The Little Mermaid (den Lille Havfrue) : The symbol of the city sited at the entry of the port, impossible to miss !

 - Nyhavn : may be the more typical neighborhood of the city, with nice boats, restaurants, Christmas market...

 - Strøget : The main (commercial) street

 - Christianshavn : a quiet and nice section of the city (Churck of Salvation / Vor Frelser Kirke)

 - Christiania : Marginal area... Difficult to describe but do not miss it ! :o)

 - Tivoli Gardens : Extraordinary (but expensive !) amusement park in the downtown ! A beautiful place well decorated with a lot of shops, rides, restaurant... It is probably better during Christmas time and especially by night ! 

 - ...

At last do not forget to taste the red grilled sausage ! ;o)

Downtown

Downtown

Downtown

Downtown

Nyhavn

The Little Mermaid

Danish Guard

Rosenborg Castle

Round Tower

University

Christianshavn

Christianshavn

Christianshavn

Typical Bike

Christiania

Christiania

Tivoli Gardens

Tivoli Gardens

Tivoli Gardens

Tivoli Gardens

Some Links :

Useful :

To Visit :

More :

Denmark

Visit Denmark

Visit Copenhagen

Danish Railway

Rejseplanen

Mermaid Sculpture

Tivoli Gardens

Christiania

Rosenborg Castle

The Round Tower

Cathedral of Copenhagen

Air France

Scandinavian Airlines

Maersk Air

Bycyklen

Christiania Bikes

Use It