• Go to the Kongens Nytorv and Nyhavn (they are at the end of the walking street)
  • Go to Nørrebro to see Copenhagen's Arabic side and to eat some great falafel and shawarma
  • Go on a canal trip. The boats leave downtown by Gammel Strand, just in front of the parliament Christiansborg. They also leave at Nyhavn. Or by Holmens Kirk (church).
  • Go up to the top of Our Saviours Church (Vor Frelsers Kirke) to get a good overview of the city. It's funny because the stairway is on the outside. (Or go up the Round Tower for a view.) For a nice cafe, go to the top floor of the Post & Tele Museum in Købmagergade. Great view and nice mood. 
  • Go to TIVOLI, one of the oldest amusement park in the world and right in the center of Copenhagen. You can't miss it. Also has beautiful old gardens royalty used to enjoy and still do (but now commoners do too)
  • Go see the palaces (Amalienborg/Rosenborg) and the parliament building (Christiansborg - this one is by the walking street too) 
  • Go see the Black Diamond, the gorgeous royal library that was renovated and extended (old building is fused into a new black glass construct by the harbour absolutely gorgeous. Make sure to go there on the hour  i.e. when it strikes 1 2 3 4 o'clock, because then they have this awesome ethereal music playing).
  • Join a Copenhagen Free Walking Tours. They tour everyday at 11am meeting at the town hall square and have excellent reviews on Tripadvisor.