Rundetaarn is a good opportunity to see Copenhagen from above - in clear weather it is possible to see to the outskirts of Copenhagen, Øresund as well as Sweden. Expect the ascent to take about 5 minutes. On top of the tower Copenhagen University has a observatory, and furthermore you have the possibility to see a small exhibition of the towers history, etc.
I'm a local, and I've been there a few times :)
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