The Barker Dam loop trail in Joshua Tree National Park is often suggested for those with children since it is an easy 1.5 mile loop. The trailhead is east to find since it is right at the Barker Dam parking lot. You can also take the spur path off the main loop to see pictographs and petroglyphs and there are plenty of boulders for kids to climb to expel any excess energy they may have.
While it is also possible to walk across Barker Dam, this activity is better suited for those that are older and have no fear of thin walking uneven paths with a drop off on either side as this video shows:
Photo courtesy of Omar Omar