The quieter reaches of the Shenandoah (before the rapids!) are lovely for family paddling trips. The Route 7 (Virginia) bridge over the Shenandoah is an easy put-in, and gives a nice 4-6 hour trip to the Route 9 bridge take-out outside Charles Town, WV. There are several beaches and small islands to stop for a picnic or explore. Bald eagles, heron colonies, beaver dams abound, as do impressive rock outcroppings in the summer months. A few riffles give the kids a thrill, but nothing too threatening.
Route 7, Berryville VA, to Route 9, Charles Town, WV
From Leesburg, take Route 7 West towards Berryville. Put-in is on the south side of the bridge, Leesburg end.