Kate's Falls is located off of Glade Creek.  It can be accessed from the Glade Creek Trail from two directions.  You can take the long way, about 4.5 miles one way.  Follow the directions to the trailhead to Glade Creek Trailhead and follow the trail up stream.  The short way is a little over a mile.

*"To get to the lower trailhead at Glade Creek Campground:

From Beckley
From Route 19 (Eisenhower Drive), take Route 41 north toward Prince. Turn right onto the Glade Creek Road, just before the bridge at Prince. Follow the gravel road seven miles; it ends at the Glade Creek trailhead.

From Fayetteville
Follow Route 19 south; take the Glen Jean exit. Turn right onto Route 61 south; follow Route 61 for 2.8 miles. Turn left, staying on Route 61, and continue for another 4.6 miles. Turn left onto Route 41 north; follow Route 41 for 4.0 miles toward Prince. Turn right onto the Glade Creek Road, just before the bridge at Prince. Follow the gravel road 7.0 miles; it ends at the Glade Creek trailhead.

To get to the Upper Trailhead:

*A high clearance four wheel drive vehicle is recommended for this road; be prepared for steep terrain, tight switchback curves, and muddy conditions.

Take Grandview exit 129 off I-64. Turn south on WV Route 9. Travel 0.5 miles toward Little Beaver State Park (junction with WV Route 307 in 0.3 miles). Turn left onto unmarked gravel road (just before Fire Tower Road). Follow this road down to Glade Creek (about one mile). Cross the bridge for trailhead parking.

 

waterfall

Kates Falls Trail

This is a very short 2/10 mile, steep spur trail leading from the Glade Creek Trail to Kates Falls"*

https://www.nps.gov/neri/planyourvisit/glade-creek-trails.htm

Photos and directions courtesy of NPS.  See the above link for more information on Glade Creek Trails.