May 09, 2018 · Milepost 305.1. US-221, which used to carry the parkway before the viaduct was built, leads a mile south to 5,946-foot Grandfather Mountain (828/733-4337 or 800/468-7325, daily, $20 adults), the highest peak in Blue Ridge, now a private park with nature trails, a zoo, and the famous Mile-High Swinging Bridge. The famous Mile-High Swinging Bridge.