If you're looking for a meeting place or a good stop around ½ or halfway between Ashburn and Jefferson City, TN, you can try Roanoke, VA, which is about 3 hours southwest of Ashburn, or almost 4 hours northeast of Jefferson City, TN.
Another possible place to stop near the midpoint is Blacksburg.
About ⅓ or a third of the way, you can stop at Staunton, VA. This is about 2 hours southwest of Ashburn.
About ⅔ or two thirds of the way, you can stop at Pierce Mill, VA. This is about 4½ hours southwest of Ashburn, or about 2½ hours east of Jefferson City, TN.
About ¾ or three fourths of the way, you can stop at Bristol, TN. This is a little over 5 hours southwest of Ashburn, or about 1½ hours northeast of Jefferson City, TN.
If you drive straight through without stopping at all, the total distance is 441 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 6 hours, 49 minutes.