If you're looking for a meeting place or a good stop around ½ or halfway between Pataskala and Nashville, you can try Louisville, KY, which is a little over 3 hours southwest of Pataskala, or almost 3 hours north of Nashville.
About ¼ or a fourth of the way, you can stop at Cincinnati, OH. This is almost 2 hours southwest of Pataskala.
About ⅓ or a third of the way, you can stop at Florence, KY. This is a little over 2 hours southwest of Pataskala.
About ⅔ or two thirds of the way, you can stop at Elizabethtown, KY. This is almost 4 hours southwest of Pataskala, or a little over 2 hours northeast of Nashville.
About ¾ or three fourths of the way, you can stop at Glasgow, KY. This is about 4½ hours southwest of Pataskala, or about 1½ hours northeast of Nashville.
If you drive straight through without stopping at all, the total distance is 398 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, 59 minutes.