Beckley's strongest sights split neatly between coal heritage and New River Gorge scenery. Start underground at the Exhibition Coal Mine, especially if you have not seen a coal camp interpreted by people who grew up around the industry.
Grandview is the easy outdoor half of the visit. It is part of the national park, but Beckley is the closest city of any size, so the overlook and rim trails belong naturally in a Beckley day. Tamarack rounds things out with West Virginia crafts and regional food when the weather turns or you want a less strenuous stop.