A walk down the pedestrian street "Stroeget" from the Town Hall to Kgs Nytorv is a must. "Stroeget" can be very crowded so donīt forget detours down some of the surrounding streets: Larsbjornstraede,Fiolstraede,Graabroedre Torv, Koebmagergade just to mention a few.

Another highly recommended walk be from Kgs Nytorv, down Nyhavn, follow the harbour front past the Amalienborg (Royal castle - guard change at 12 noon), The Resistance Museum,Kastellet and on to the Little Mermaid.
Further on you will come to Langelinie, where most of the cruise ships harbour.
And Tivoli of course - go there at night when all the lights are on.

See http://www.aok.dk/section/english, for whats up in Copenhagen.

Enjoy - the weather is just great here for the time beeing.