(37.775318, -81.155487)

A good place to park is at the western lot of the soccer complex.  It's at the inrtersection of YMCA Dr. and YMCA Dr. just across from a medical building.  (37.783472, -81.148381)  Look at the map below for more precise information.

JANUARY 2019 - On my visit to see the Beckley Mill, I discovered that the entrance at New Jersey Avenue is now gated.  I was miffed and upset enough to investigate, as I had spent a lot of time just getting there.  After many phone calls, I was put in touch with Tom Sopher, a councilman, who was instrumental in getting this trail system developed.  I went to visit him and we talked a long time.  The bottom line is that, if you want to visit here, you need to access the area through the YMCA property.  Not sure what their policy is on parking there, but it seems to be the spot most are talking about.  I have also noticed that there is a trail that begins off of Timberland Rd., just prior to the YMCA.  I have no direct information on this, but there is a trail there.  That's the western end of the Gray Flats Trail (No. 7) on the map below.  Not sure about the parking situation.
 
Update: April 7, 2019 - I parked on the west end of the YMCA complex, closest to the Grey Flats Trailhead. I walked down by way of trails 7, 12, 3, 9, 2, in that order.  It was not difficult to follow.  Trail junctions were marked, though not all of them terribly obvious.  I recommend printing this map and taking it with you.  Trail 2 is a wide open dirt road that follows the western side of a gorge right down into the mill area.  Falls and mill ruins are obvious and the wide open green space is a great place to rest up or have a picnic.  When leaving I followed Trail 8, which is the trail I recommend to go in and out.  You will find additional waterfalls on this trail.  Its the trail you would see on the other side of the gorge from Trail 2.
 

From the Beckley Convention Center on US 19, drive south on US 19 for 0.4 mile. Turn left onto New Jersey Avenue, and an immediate left on Joe L. Smith Drive/E. Beckley ByPass. Continue for 0.8 mile and turn right on YMCA Dr.. There will be a big parking lot on your right, just next to a soccer field.  Park there.  Walk across the field, crossing the road you came in on, and start down Timberland Rd. Walk down Timerland Rd. and go right on Stone Cir. Rd.  At the end of the road in a culdesac, the trail begins.  This is Trail #7.  I think it also starts on Timberland Rd. but I did not see it.  It probably starts at the edge of the wooded area behind the houses on Stone Cir. Rd.  Follow the trails listed above in the April 7, 2019 update and that will take you down to a great picnic spot and the Beckley Mill Falls.

From I-64, exit 124, follow the Joe L. Smith Dr. to a right on Jersey Avenue and an immediate left on Joe L. Smith Drive/E. Beckley ByPass. Continue for 0.8 mile and turn right on YMCA Dr..

GPS for the falls/mill: 37.773376, -81.150353

The Beckley Mill Site was officially listed May 1, 2017 in the National Register of Historic Places, United States Department of the Interior, National Park Service.  The City of Beckley hosted a ribbon cutting at the newly created parking area for the Beckley Mill and its trail head, (the trail leads to the Mill Site ruins on the banks of Piney Creek), Saturday at 2:30 pm, 27 May, 2017, as part of the Raleigh County Historical Society's Founder's Day Celebration.

The half-mile trail descends steeply from the margins of the City of Beckley to the banks of the Piney Creek and is part of a system of trails opened in and near the Piney Creek Gorge.  The trail-head parking area is on New Jersey Avenue.  The trail has been designed to accommodate hikers and bikers and provides access to a large natural area along the creek that includes two waterfalls. The trail also connects with trails that wander the Grey Flats area near the Beckley YMCA Soccer Complex.

Info courtesy of WV Explorer

There are obviously more waterfalls down here on the Piney Creek.  Here are some examples as posted by Anna Stables on the West Virginia Waterfalls Facebook Group.

BeckleyMill05

BeckleyMill04

BeckleyMill01

BeckleyMill02

BeckleyMill03

PineyCreekMap