If you're looking for a meeting place or a good stop around ½ or halfway between Mechanicsville and Lincolnia, you can try Massaponax, VA, which is almost an hour north of Mechanicsville, or almost an hour southwest of Lincolnia.
Other possible places to stop near the midpoint include Bellvue, Leavells, and Concord Heights.
About ¼ or a fourth of the way, you can stop at Caroline Pines, VA. This is about half an hour north of Mechanicsville.
About ⅓ or a third of the way, you can stop at Patersons Corner, VA. This is about half an hour north of Mechanicsville.
About ⅔ or two thirds of the way, you can stop at Stafford, VA. This is almost an hour north of Mechanicsville, or about half an hour southwest of Lincolnia.
About ¾ or three fourths of the way, you can stop at Midway Island, VA. This is about 1 hour north of Mechanicsville, or about half an hour southwest of Lincolnia.
If you drive straight through without stopping at all, the total distance is 96 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 1 hour, 30 minutes.