National Park de Hoge Veluwe is the big nature excursion from Arnhem: a broad protected landscape of heath, pine forest, shifting sand, and grassland on the Veluwe. The park is famous for its free white bicycles, which make it easy to cover more ground than you would on foot.
The strongest visit combines cycling with the Kröller-Müller Museum, just inside the park, whose Van Gogh collection and sculpture garden are reason enough to come. Start early if you want both art and landscape in one day, and leave time simply to ride through the open heath rather than rushing from one attraction to the next.