One thing you won't hear talked about much is that Copenhagen serves as the home of the world's most accurate mechanical clock. This differs from the world's most accurate clock overall which is atomic and not based in Denmark.
The clock is on display just inside city hall and open to the public.
Built by Jens Olsen the clock is re-wound once a week, has the slowest turning gear in the world, and is gilded with four kilos of gold. It was first started in 1955 and also displays the location of the planets as well as the stars above city hall.
Open to the public, Copenhagen City Hall has a number of extremely unique and charming art installations. This photo features an early depiction of Copenhagen which is frescoed onto the walls and ceilings of the stairwell. The stairwell on the opposite side has a large maritime/sea monster themed tile mural.
To glimpse this piece of Copenhagen's past, walk in City Hall's front doors, and cut left across the large open interior chamber. Then take the stairs to the top floor.