There is an existing problem of what to do when visitors come to Copenhagen.
Personally, I encountered so many fantastic sites that it is practically impossible to decide for me what my guest should see- everything seems to be equally important and worth seeing.
I had to come to a compromise- choose what is the most important ( must-sees)+interesting+entertaining. This is a short advice for those who are struggling to entertain their guests.
FOR A SHORT STAY
*Canal tours (http://www.canaltours.dk/dct/da) perfect to see everything: starting from Nyhavn ( old sailor/red light district) going to see the Opera ( new 14 storey building with 5 levels under water), Amalienborg ( Queen’s residence), The little Mermaid, Black Diamond and many more. Takes an hour and is around 60 dkk. Worth it!
* Stroll around Stroget, well after all it is the main shopping district and the building are quite interesting. For those who prefer more cosy and less commercial atmosphere just go onto the parallel street to Stroget: running to the South STRAEDET– many bars and little boutiques. Also an excellent jazz bar La Fontaine (http://www.lafontaine.dk/ ), good entertainment for the evening.
where to eat with your guests? well, if you are active visitors you would like to see as much as you can, then just rely on the hot-dog stands. I would suggest the ones with red-yellow colors and name “Tulip”, the other are blue red and white, I guess.
In the center: Close to Norreport station- Kalaset cafe. Always a good bet.
FOR A LONGER STAY
Then you have a whole variety. However, things which are exciting and a bit further from Copenhagen are:
*LOUISIANA MUSEUM (http://www.louisiana.dk/dk) – Museum for Modern Art. you have to take a train to Humlabaek ( half an hour from Central Copenhagen) have a 10 min walk and there you are: fantastic building with a great garden by the seaside with all kind of forms of art: sculptures, mirror toilet and a square for kids.
* A trip to Sweden, just half an hour and you are in another country! Malmo Central is the closest stop and it is worth seeing- a bit industrial but still charming. At the train station go to the tourist office and ask for a map and there you have all the must-sees: main square, design centre and famous Torso. From Malmo- next stop LUND. Charming town of 90 000 inhabitants and great academic atmosphere from XVIIth century. Different times!!!