When we arrived in the city center after transferring from the airport in train & metro, we directly saw the guards heading to the queen's palace of Amalienborg. At noon, we saw guards formal presentation.
We then went to our Hotel at the end of the Nyhavn docks.
In the afternoon, we decided to walk down Stroget, the main commercial street of Copenhagen. The street is reserved to pedestrians and leads from Nyhavn and Kongens Nytorv to Town Hall (Radhus) and its large place. There is a number of places to admire along the walk, amongst which the nice storks fountain.
On sunday, and despite a battling rain, we walked to see the little mermaid. In the middle of a tourists host, we could manage to take a picture of the mermaid, who is indeed little. On the walk back, we admired the very nice Gefion fountain and passed back the Kastellet, oldest barracks still in use in Europe. We also visited the "marble church", interesting both for the size of its dome and the number of its large statues.
At the end of the afternoon, we entered the famous Tivoli Park, where we experienced the "Starflyer", a 80m high carousel ! We also had a nice dinner in one of the numerous Park's restaurant.
On monday, we chose to rent a car and drive in the surroundings. We drove along the Oresund coast to Helsingor. It is astonishing to see how close we were from the swedish coast, despite the large sea vessels passing by to reach the baltic sea.
In Helsingor, we visited the outside of Kronborg citadel, which used to defend the entrance of the Oresund.
We then drove to Hillerod, where we visited the royal palace of Frederiksborg. Building is indeed very nice, in the middle of large gardens. Inside decoration is great, only some rooms have furniture but there is a very large pictures collection.
Our final step before moving back to Copenhagen was Roskilde, where we arrived at the end of the afternoon. We could not visit the city but spent some time in the Viking ships museum. The 5 original Drakkars the scientists pulled out of the Fjord ground are not really that impressive but the museum is very well arranged : a bunch of explanations, models, exhibitions, even reconstituted viking ships in the museum harbors, in which you can have a tour!
To wrap it up, 2 days are fine to visit Copenhague itself. We had very bad weather (in August!) and in overall, life is very expensive in Denmark, both for dining and hotels.