Skyline Drive is part of Shenandoah National Park in Virginia. There is a fee to enter it. There are many stops to pull over for viewing and to rest for a while. There are bigger picnic areas, but they have their own parking lots and not directly on a mountain-side. I did see a bear crossing the road and it was probably close to 300lbs, so do follow the guidelines to store and dispose your food properly.
There are several wayside stops with park buildings including restuarants and lodging. “Skyland” is the stop at the highpoint on the trip. I drove from north to south and might be predjudiced, but I believe there were better views north of Skyland. In any case, one afternoon isn’t really enough. You can spend days exploring this park.