We decided to go on a boat tour on the spur of the moment; we were too late for the tour that was leaving right at that moment, but the departure location is a great place to chill out in front of the water.
We had a fantastic time with our captain Ilona - she was interesting, warm, open and fun; we felt like we were learning about and connecting with the place, whilst not feeling like we were on museum tour.
Although possibly more expensive than a mass tourist boat, you get the benefit of the personal interaction, real conversations about Copenhagen as opposed to a monologue... we should also mention the wine; one generally expects that wine comes with this sort of your is rough plonk, but it was really rather good and perfect for an afternoon on the water - we were also assured that it had been QA'd by the captains themselves after hours!
Ilona also recommended some restaurants for dinner, one of which we went to and had a great last meal in the city; there are so many to choose from that we really appreciated some insider information and were not disappointed.
We would recommend this tour (and have done so to our friends) for anyone passing through Copenhagen, or even there for for longer.More