If you're looking for a meeting place or a good stop around ½ or halfway between Pataskala and Zanesville, you can try Atherton, OH, which is about 18 minutes east of Pataskala, or about half an hour west of Zanesville.
About ¼ or a fourth of the way, you can stop at Har-Win Acres, OH. This is about 10 minutes east of Pataskala.
About ⅓ or a third of the way, you can stop at Hebron, OH. This is about 14 minutes east of Pataskala.
About ⅔ or two thirds of the way, you can stop at Brownsville, OH. This is about half an hour east of Pataskala, or about 14 minutes west of Zanesville.
If you drive straight through without stopping at all, the total distance is 39 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 41 minutes.