The Hoge Veluwe National Park, which was once the private property and hunting grounds of the Kroller-Muller family, is now the largest national park in the Netherlands and can be easily transversed on foot or by bike without impediment. It offers endless moors, vast forests, and expanses of grasslands and sand drifts.
The best aspect of the park is the 1,000 white bicycles that are free to visitors. The park has over 42km of scenic cycle paths, and visitors can pick up bikes at any entrance to the park or at the visitor center. Specially adapted bicycles for disabled visitors are also available. I spent a whole day here riding bicycles through the park, eating alfresco at one of the two restaurants, and exploring the Kroller Muller Museum, which houses one of the world's largest collections of van Goghs and a sculpture garden featuring Rodin (among others). See my separate write-up for the museum. There is also an excellent visitor center, where you can learn more about the nature, landscape, wildlife, culture, and history of the park.
This is a great cultural "day away" for the family, as you can easily combine outdoor explorations and riding bikes with a heavy dose of art. What a combo!