Shenandoah National Park Fee Free Day in Honor of Park Neighbor Day. 7AM. Shenandoah National Park will waive entrance fees for all park visitors on Saturday, June 17 in celebration of Park Neighbor Day, an annual event held on the third Saturday of June to honor our neighbors who live in the counties and gateway communities surrounding the Park. Free displays, hikes, kids activities. 540-999-3500. http://www.nps.gov/shen/index.htm Skyline Drive, Afton, VA, 22920.