Amsterdam's forest is a vast swathe (roughly 1000 hectares) of almost countryside, 20 minutes by bike south of Vondelpark. Planted in 1934 to provide employment during the Great Depression, its lakes, woods and meadows are criss-crossed by paths and dotted with cafes. You can rent bicycles, feed baby goats in spring, take a horse-riding lesson, boat the rural-feeling waterways, see a play at the open-air theatre and ascend to the treetops in the climbing park.
It's a glorious place to go with kids, though best if you explore by bike due to its size. There's a bike rental kiosk across from the forest entrance and a visitor centre with information. In the densest thickets you forget you're near a city at all (though you're right by Schiphol airport). A lot of locals use the park, but it rarely feels crowded.