Rosenborg Castle is so preposterously pretty it looks like an illustration from a fairy tale by local hero Hans Christian Andersen. Built around 1606, it’s surrounded by a moat and is topped off with verdigris-covered towers and turrets. The beautiful gardens—the oldest royal gardens in Denmark—feature box hedges clipped into star patterns. The only downside is that the castle can often be crowded with visitors who come to see the Danish crown jewels and throne.