Kelly Knob Overlook is about seven miles north of Newport, Virginia. From Blacksburg, take US-460W for 8 miles, turn right on VA-42 E/Blue Grass Trail, turn left on Clover Hollow Rd/State Route 601, and continue on it for 6.7 miles until it reaches an intersection with the Appalachian Trail. Primary activities include hiking and dog walking. Parking was free but limited to two to three cars. Water and restrooms were not available. Cell phone service was intermittent while on the trail.
The hike to Kelly Knob Overlook followed a 2.0 mile segment of the Appalachian trail. The first half mile was a steep incline after which the slope leveled off. The following chart shows the relative change in elevation, starting at 3,100 feet and leveling off at around 3,600 feet.
The following picture illustrates the incline of the first half mile. If your kids can make it up this incline then the rest of the hike should be easy for them, minus a few rocky sections. I carried our daughter in a child carrier backpack so this first stretch was challenging for me.
The latter 1.5 miles rolled up and down gradually and included both smooth and rocky sections. It was a peaceful walk because the limited parking reduced the chance that we’d be sharing the trail with a crowd of people. We followed the Appalachian Trail white blaze markers until we saw a sign for the overlook.
From the sign pointing to the overlook, we followed blue blaze markers 120 yards. Up to this point, the forest canopy was dense and, thus, it provided shade on a sunny day.
We hiked this on a very hot and hazy August day. Our view was limited so I recommend visiting on a clearer day. Further, it felt significantly hotter at the overlook than it did on the trail so we did not stay long. I imagine Autumn colors would be a treat to see from this spot.
The overlook had space to set up a picnic but it was rocky and precarious to walk on. The following video scans 360 degrees from the center of the overlook.
In sum, the hike to Kelly Knob Overlook was fun, peaceful, and moderately challenging. Similar trails nearby include Angels Rest, Cascades Waterfall, McAfee Knob, and War Spur Loop.
Two Knobby Tires 
I will add to your directions, as we hiked there today. At one point on Clover Hollow Road (about 4 miles?), the road takes a sharp left by a farmhouse. A gravel road continues straight, called Laurel Springs Road. You have to stay on Laurel Springs for about 1.5 miles. There is a small parking lot (on the top of a little hill, left side) which is not marked. The AT crosses here (white blazes), and you have to hike up the hill across from the parking lot (approximately east, or north on the AT).
Thank you for your more detailed directions!