This is a nice waterfall. There is room to pull off the road and park and a short steep trail down to the water lever. This might be private property, but seems accessible and often visited. If you have been to Drawdy Falls, this is just down the road, so, it's easy to get to from there.
From Charleston take I-64 toward Beckley and get off at Exit 89. Go south on Lens Creek Road, SR 94, to Racine and bear right on SR 3. Drive 2 miles and turn right on Costa Rd. Drive 1.2 miles and bear left onto Middle White Oak Rd.
From Beckley use the same directions as for Peachtree Falls and continue on SR 3 for 33.6 additional miles from the place where you turn off to cross the bridge to Peachtree Falls and turn right on Costa Rd. Drive 1.2 miles and bear left onto Middle White Oak Rd.