If you're looking for a meeting place or a good stop around ½ or halfway between Laytonsville and Sterling, VA, you can try Potomac, MD, which is about half an hour south of Laytonsville, or about half an hour east of Sterling, VA.
Another possible place to stop near the midpoint is Carderock Springs.
About ¼ or a fourth of the way, you can stop at Rockville, MD. This is about 12 minutes south of Laytonsville.
About ¾ or three fourths of the way, you can stop at Reston, VA. This is about half an hour southwest of Laytonsville, or about 12 minutes southeast of Sterling, VA.
If you drive straight through without stopping at all, the total distance is 42 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 51 minutes.