The Round Tower and Planetarium
The Round Tower
It's located in the center of Copenhagen, on the pedestrian street between the Nørreport station and the Stork Fountain.
The tower was built in connection with the Trinitatis Church. I like churches and this is a beautiful one.
But really beautiful is the view from the top of the tower. The city is quite flat and from the top of the building you can see many places of interest. Walking up is easy as there is a ramp almost all the way to the top.
Here is a link to a nice website about the tower.
Tycho Brahe Planetarium
In the center of the city, by the St. Jorge Lake (Sankt Jørgens Sø). If the name Tycho Brahe doesn't ring a bell, he was a famous Danish nobleman and astronomer.
The films are presented in IMAX. Each presentation starts by showing the stars and explaining a little about them. Unfortunately most presentations are narrated in Danish.
The restaurant here is actually good and not too expensive.