Take US276 beginning in Brevard, NC and travel south just across the NC/SC border at Caesar's Head State Park.
The route begins in the French Broad River Valley at Brevard, NC. Picturesque farms quickly transition to mountain cabins as you climb towards the South Carolina border. There are views across the valley, but very few places to pull over and enjoy them. At the end of the route take a right turn into Caesar's Head State Park. This is worth some time off-the-bike. Follow the signs along a walking path to an overlook. On a clear day you will be able to see more than 50 miles. Looking west, in the distance, you are viewing the southern foothills of the Blue Ridge Mountains.
The road is seldom busy. The ascent is quick, with most of the curves easy to negotiate without having to downshift. Lack of traffic and the ability to take turns at full throttle make for a fun ride.
Caesar's Head State Park is were you will want to dismount and look around. The park has picnic tables, a small gift shop and plenty of long range views. I suggest grabbing a to-go lunch from Big Mike's Diner in Brevard, NC (only 17 mile away) and enjoying it while watching the clouds roll across the Blue Ride Mountains.