If you're looking for a meeting place or a good stop around ½ or halfway between Fayetteville and Villa Rica, you can try Augusta, GA, which is a little over 3 hours southwest of Fayetteville, or almost 3 hours east of Villa Rica.
Other possible places to stop near the midpoint include Lexington, and Aiken.
About ¼ or a fourth of the way, you can stop at Lewis Crossroads, SC. This is about 1½ hours southwest of Fayetteville.
About ⅓ or a third of the way, you can stop at Columbia, SC. This is a little over 2 hours southwest of Fayetteville.
About ⅔ or two thirds of the way, you can stop at Tatham Mines, GA. This is almost 4 hours southwest of Fayetteville, or a little over 2 hours east of Villa Rica.
About ¾ or three fourths of the way, you can stop at Eatonton, GA. This is about 4½ hours southwest of Fayetteville, or about 1½ hours east of Villa Rica.
If you drive straight through without stopping at all, the total distance is 408 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 5 hours, 58 minutes.