If you're looking for a meeting place or a good stop around ½ or halfway between Ashburn and Beckley, you can try Summerdean, VA, which is about 2½ hours southwest of Ashburn, or a little over 2 hours east of Beckley.
Other possible places to stop near the midpoint include McKinley, and Greenville.
About ¼ or a fourth of the way, you can stop at Stephens Fort, VA. This is about 1 hour west of Ashburn.
About ⅓ or a third of the way, you can stop at Harrisonburg, VA. This is about 1½ hours southwest of Ashburn.
About ⅔ or two thirds of the way, you can stop at Millboro, VA. This is almost 3 hours southwest of Ashburn, or almost 2 hours east of Beckley.
About ¾ or three fourths of the way, you can stop at Baldwin, VA. This is a little over 3 hours southwest of Ashburn, or a little over 1 hour east of Beckley.
If you drive straight through without stopping at all, the total distance is 287 miles. The distances shown above don't include local roads to get into each town, so if you're planning a long road trip, make sure you factor in traffic and road conditions, rest stop breaks, and interesting detours along the way. If you're in a rush, you can do the trip with zero stops, and your total travel time would be around 4 hours, 31 minutes.