"The Round Tower" - I visited it a couple of years ago. You can read the details here of the observatory:
http://www.rundetaarn.dk/en/the-observatory/
Most of the way up the tower is a winding ramp (see image here:
http://www.rundetaarn.dk/en/the-tower/). One of the interesting tales is about Peter the Great - he road his horse up the tower with his wife in a carriage following. No idea how they got the carriage back down. (
http://www.rundetaarn.dk/en/the-towe...-on-horseback/)
From the observatory deck level itself, you can get good views of Copenhagen, weather permitting.