If you're looking for a meeting place or a good stop around ½ or halfway between Poolesville and Grove City, you can try Washington, PA, which is about 3½ hours northwest of Poolesville, or about 3 hours east of Grove City.
Other possible places to stop near the midpoint include Arnold City, Rankins Corners, Turkeyfoot, and Coal Center.
About ¼ or a fourth of the way, you can stop at Cumberland, MD. This is about 1½ hours northwest of Poolesville.
About ⅓ or a third of the way, you can stop at Pleasant Union, PA. This is about 2 hours northwest of Poolesville.
About ⅔ or two thirds of the way, you can stop at Wheeling, WV. This is about 4 hours west of Poolesville, or a little over 2 hours east of Grove City.
About ¾ or three fourths of the way, you can stop at Cambridge, OH. This is about 4½ hours west of Poolesville, or about 1½ hours east of Grove City.
If you drive straight through without stopping at all, the total distance is 383 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, 12 minutes.