On a visit to Copenhagen, I visited Kastellet (wich means "the citadel" in Danish).
Kastellet is a fort built between 1626 and 1640. It is a star-shaped fort like most of the forts built during this period.
Here is an aerial view of Kastellet.
The red cross on the picture indicates the location of the Little Mermaid statue. As you can see they both are very close to each other.
Now some history:
After the swedish siege of Copenhagen, Kastellet was rebuilt and extended between 1658 and 1660. It helped in the defense of Copenhagen against England in 1807 during what is called "the battle of Copenhagen". In April 1940, the German troops captured Kastellet resulting in the capitulation of Denmark.
Nowadays, Kastellet is still a military area but is open to public.
Personal thoughts :
I wouldn't recommend visiting Kastellet unless you have an interest into Danosh history or is interested by this kind of architecture.