The Kancamagus Highway in peak foliage season. Alamy Stock Photo It’s 10 a.m. on a Saturday and a sign already sits in front of the Lincoln Woods Trailhead: Parking Lot Full.

Recognized as a National Scenic Byway for its stunning views, the Kancamagus Highway runs 34.5 miles from the town of Lincoln toward Conway. As the route cuts west-to-east across the state, it ...