Free camping near, but not on the river
This is another of the free national park campgrounds in the New River Gorge, with sites that are more developed than many of the others. These are in a small open loop, largely level gravel parking and tent pads. They have picnic tables, fire rings, and lantern poles. No drinking water, so bring your own. No hookups. The river is nearby, but none of the sites are on the river. There’s an accessible site and also accessible trail to a bench along the river. There are latrines.
If you enjoy fishing, the New River Gorge website offers a lot of specific information about species, bait, and lures.
If you can't find a site at one of the other campgrounds or you have a slightly larger rig, ths may be a better option for you. No cell service, so download your maps. The New River Gorge also offers rafting, and hiking options. Check out some of the mining history at the Beckley Exhibition Coal Mine, abuut 30 minutes away, and get up early to catch the sunrise from Grandview Point.