Two harbour tours leave from Nyhavn, one for 60 and one for 30 Kroner. I did the cheapest and thought it was excellent. Good commentary and overview of the city, loads of inspiration for things to see the next day.
Yes, yes I know --- this is quite touristic but as usual when you need some rest just do it !
It's an hop-by-hop tour so you can drop off the bus where you want and come back at the next.
BTW: I consider the city giving the best at peripherals areas, this is the best "tool" to discover them.
If you have seen some of my other pages you will have noticed that I like taking these City Sightseeing hop-on hop-off bus tours. And that is because they are a great way to see a new city. They are flexible in that if you see something you like you can jump off the bus at the next stop, they hit all the main sites in the city, and the tours are available in multiple languages.
There are three different routes through the city: the Mermaid Tour, the Carlsberg Tour and the Christiania Tour (only available with the combination ticket). You can do the Mermaid Tour or Carlsberg Tour on their own and it will cost you 120 DKK for Adults and 50 DKK for Children (for each tour and lasts for 24 hours). Or you can do all three tours, buying a combination ticket, that costs: 140 DKK for Adults and 70 DKK for Children, and it is valid for two days. Each (individual) tour takes an hour for it to complete its circuit.
If you just want a quick trip around the city centre to see the main sights (Rådhuspladsen, Tivoli, Kongens Have, Kastellet, the Little Mermaid, Amalienborg and Kongens Nytorv) then take the Mermaid Tour. But if you are staying longer and are interested in trips out to the Carlsberg factory, the Zoo, or over to Christiania, then I recommend you buy the combination ticket.
Tours are multi-lingual (pre-recorded) and are available in: Danish, English, Swedish, Norwegian, German, French, Russian, Italian, Spanish and (for some tours) Polish.
Start by getting on to one of the City Sightseeing buses, they stop at the best sights, and give a lot of information.
Very interseting places. There are stopovers at harbours and museums, and parks if you just want to enjoy the weather on a good day.
Walking tour of the old Copenhagen
I joined one of the guided walking tour of Old Copenhagen (they live every morning from the tourist information office near Tivoli). It was very interesting, I learnt a lot about the city and his history, and many unusual things.
I liked this statue: it's a woman selling fish, a very traditional activity in Denmark.
not that cheap, but to see a lot of Copenhagen in few time the sightseeing tours are a good alternative.