Fredensborg Palace Garden is one of Denmark's largest baroque gardens, arranged around long straight avenues that pull the eye away from the palace towards the surrounding woodland. It is less theatrical than Versailles-style gardens and more Danish in temperament: clipped geometry, open lawns, big trees, and enough informality to make it pleasant rather than stiff.
The public garden is open through the year, while the reserved royal garden is normally visited only on guided tours in summer. Give yourself at least an hour. The best part is not any one monument but the rhythm of the place: palace, avenue, grove, lake air, then back again.