There are a lot of cruise ship tourist, and others that only want to see the guidebook classics. Here is a short introduction.
Nyhavn
A tourist trap. If you google Copenhagen, eight out of ten pictures are from Nyhavn. You just walk around taking pictures of the nice houses, with a lot of tourist on them. And the bars and restaurants are overpriced. A few serve decent food, but the rest is shitty. It is the most visited attraction in Denmark. Kunsthal Charlottenborg, the art school is there, and it can be worth visiting.
The Little Mermaid
It is a very small statue, by the harbour. And there are a lot of people standing there taking pictures. It is on the list of the ten most diapointing tourist attractions in Scandinavia. And there is a souvienir stand next so it. If any Danish media brings pictures of the statue, they have to pay to the ancestors of the guy who build it. Therefore, no pictures here on the website
We are still stuck with the little Mermaid as brand of Copenhagen.
Tivoli
An amousment park right in the city center, next to the Town Hall Square. It is expensive and crowded, and you mostly meet other tourist. When my daughter was 12-13 years old, she had a platin card, allowing here, to go after school, and try out as much as she liked.
If you have kids, you might have a good time here, specially in the midday. But you will end up spending a fortune.
Amalienborg
Is the official residence of the Royal family. A lot come here at 12 o´clock , midday, to witness the changing of the guards. Dont do it: It is just soldiers coming with there uniforms and guns, and taking a walk around the square. And you cant see anything because of the crowd. If you are lucky they bring a band.