If you're looking for a meeting place or a good stop around ½ or halfway between Tallahassee and Panama City Beach, you can try Leonards, FL, which is about 1 hour west of Tallahassee, or a little over 1 hour northeast of Panama City Beach.
Other possible places to stop near the midpoint include Ocheeseulga, Clarksville, and Rollins Corner.
About ¼ or a fourth of the way, you can stop at Lowry, FL. This is about half an hour west of Tallahassee.
About ⅓ or a third of the way, you can stop at Hosford, FL. This is almost an hour west of Tallahassee.
About ⅔ or two thirds of the way, you can stop at Fountain, FL. This is about 1½ hours west of Tallahassee, or almost an hour northeast of Panama City Beach.
About ¾ or three fourths of the way, you can stop at Saunders, FL. This is about 1½ hours west of Tallahassee, or about half an hour northeast of Panama City Beach.
If you drive straight through without stopping at all, the total distance is 106 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 2 hours, 16 minutes.