The Rose Benchmark marks the highest elevation of Braxton County, WV at 2,183 feet. It is the 28th highest county highpoint in WV. This is a pretty nondescript locale. Nothing to really see and isn't really a hike of anything worth mentioning, but if you desire to visit all of the county highpoints in WV, then I suppose you're going to have to check it out, at least before the surrounding strip mine operations consume it.
From the small town of Birch River, go north on rt. 19 to Old Turnpike Road (CR 19/40) on the right. Turn right and go approximately 3.9 miles to Crites Mountain Road (CR 19/35) on the right. Turn right and follow for approximately 4.1 miles to a T-intersection with a heavily travelled mine access road. Turn left and make another immediate left onto a gated gravel road. Park and walk gated road 100 meters or so to a oil/gas well. On the right, adjacant to the road and prior to reaching the gas well, is the USGS marker signifying the top of Braxton County.
As far as I know, this land is open for travel. It isn't owned by any particular entity and as long as you stay on the oil/gas well road you should be fine. There aren't any posted signs around.
Several places within a short driving distance are available for camping. Flatwoods has a KOA campground available. Bulltown Recreation Area located near Burnsville, WV has camping. Summersville Lake is located a little less than half an hour south and contains several opportunities for camping.