The waterfalls on Beckwith Road are pretty nice. This is the Laurel Creek as it tumbles downhill to the New River and there are a number of falls in this stretch of road. One thing to know about this area is that it's not exactly accomodating to parking or pedestrians. It's a very busy and winding road and people are not driving slow through here. Just be safe. The other thing is the scramble down into the creek is over some pretty jagged rocks and there's a lot of piled up lumber.
From US 19 in Fayetteville, follow SR 16 for approximately 5.5 miles and you will begin to see the Laurel Creek along the side of the road. It all begins at the gas station, where there is a dam with a falls. You can pull off on the right in a couple of places, cross the road and over the guard rail. A safer place would be to continue on down the road for another mile, cross the Cotton Hill bridge over the New River and turn an immediate right into a parking lot. Kayakers put in here, so you're liable to meet a few of them. Walk back up the road and jump down in the creek where ever you see something you like. It's a nice stretch of creek and I don't think these falls have any particular names.
If the water is flowing pretty well, you might be able to get a shot of a pretty little thing that tumbles down the side of the hill on the creek side about 100 yards down from the main falls. Just keep your eyes open as you walk down the road. It's somewhat concealed by trees and overgrowth and up on the hillside, so you can't exactly get at it. You have to shoot it from up on the road and that's probably the best view anyway.
There is also another falls downstream from this one. You'll have to walk along and find it yourself. I've seen it, but I couldn't get at it the day I was trying, so another day. I will say, I've seen photos and saw it from above and it's worth the effort.