If you're looking for a meeting place or a good stop around ½ or halfway between Ashburn and Cambridge, MD, you can try Annapolis, MD, which is a little over 1 hour east of Ashburn, or about 1 hour northwest of Cambridge, MD.
Another possible place to stop near the midpoint is Crofton.
About ¼ or a fourth of the way, you can stop at Silver Spring, MD. This is about half an hour east of Ashburn.
About ⅓ or a third of the way, you can stop at Chillum, MD. This is almost an hour east of Ashburn.
About ⅔ or two thirds of the way, you can stop at Bentons Pleasure, MD. This is about 1½ hours east of Ashburn, or almost an hour northwest of Cambridge, MD.
About ¾ or three fourths of the way, you can stop at Scottown, MD. This is almost 2 hours east of Ashburn, or about half an hour north of Cambridge, MD.
If you drive straight through without stopping at all, the total distance is 124 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 2 hours, 19 minutes.