If you're looking for a meeting place or a good stop around ½ or halfway between Rincon and Atlanta, you can try Rebie, GA, which is almost 2 hours west of Rincon, or about 2 hours southeast of Atlanta.
About ¼ or a fourth of the way, you can stop at Adabelle, GA. This is almost an hour west of Rincon.
About ⅓ or a third of the way, you can stop at Wesley, GA. This is about 1 hour west of Rincon.
About ¾ or three fourths of the way, you can stop at Whitehouse Plantation, GA. This is about 2½ hours west of Rincon, or about 1 hour southeast of Atlanta.
If you drive straight through without stopping at all, the total distance is 241 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 3 hours, 37 minutes.