if you ever come to visit copenhagen, please just walk around the city! yes, there's a metro and yes, there are busses, but just for once let go of your plans and singled out sightseeing spots and just drift along. however... when you are drifting, make sure you'll drift through pretty streets with pretty houses like magstraede and snaregade and jaegersborggade and olufsvej and... to be honest, nearly every street is worth seeing.
plus: a walk up 'rundetaarn' will not only give you a wonderful view of copenhagen, but you'll also see the sea and a tiny bit of sweden.