The Rundentaarn, or Round Tower, is... well... a round tower. Visitor can walk up the corkscrewing paved path -- not steps -- for eight "turns" to get to the top. Once there, you're rewarded with some stunning views of Copenhagen from one of the highest vantage points. Of course, the day we were there, it was windy and cloudy. Welcome to Denmark.
Traveling back down, be sure to stop off in the library/art gallery, and check out the side room where they've preserved some of the buildings history during restoration. It's worth the fairly inexpensive price of admission!