The Forêt de Venasque, criss-crossed by walking trails (including long-distance GR91), lies east of Venasque. Cross the Col de Murs mountain pass (627m) to pretty little Murs, and see remains of Le Mur de la Peste (the Plague Wall), built in 1720 in a vain attempt to stop the plague from entering papal territory.
You could also walk into the Luberon from here, calling at Gordes and Abbaye Notre-Dame de Sénanque. The map Balades en forêts du Ventoux de Venasque et St-Lambert (€8) outlines several family-friendly walks.