If you're looking for a meeting place or a good stop around ½ or halfway between Fort Washington and Ashburn, you can try West Falls Church, VA, which is about half an hour northwest of Fort Washington, or about half an hour southeast of Ashburn.
About ¼ or a fourth of the way, you can stop at Franconia, VA. This is about 16 minutes northwest of Fort Washington.
About ⅔ or two thirds of the way, you can stop at Wolf Trap, VA. This is almost an hour northwest of Fort Washington, or about 19 minutes southeast of Ashburn.
About ¾ or three fourths of the way, you can stop at Reston, VA. This is almost an hour northwest of Fort Washington, or about 16 minutes southeast of Ashburn.
If you drive straight through without stopping at all, the total distance is 50 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 59 minutes.