Open to the public
The Copenhagen City Hall, or Radhuset, stands next to Tivoli Gardens in the city center. You can see it from a distance as it's a huge red brick building with a clock tower that dwarfs everything in its surroundings. It's open to the public, so you can stroll through its rooms and admire the paintings and frescoes. You can climb the tower but you have to pay another 20 DKK. There is a nice courtyard in the center, and also a world clock created by Jens Olsen. The astronomical clock is downstairs, and it costs 5DKK to see it.