Rosenborg is a beautiful 17th century castle located right in the middle of Copenhagen, with gardens all around. What makes it even more special is that it's so lovely inside, fully furnished and very lavish, and they also house the Crown jewels of Denmark in the basement.
The gardens themselves were divine in September, with roses still out and everything beautiful and green. It was warm so the Danish and tourists alike were out sitting in the sunshine.
Inside the castle, it was just as lovely - highly recommend it if you go to Copenhagen!