"Sophienholm, definitely. It's located a little north of Lyngby and is a great place to go in all kinds of weather.
You can either enjoy the beautiful view of the lake Bagsværd Sø in the park itself or just sit with a cup of coffee and a book in the green and almost royal surroundings.
Several times a year there are free open-air concerts in all genres from jazz to classical music.
The boat ride stops right at the eatery in Sophienholm, and you can sail around the three lakes from May to September and get some of the best nature experiences."