If you're looking for a meeting place or a good stop around ½ or halfway between Pensacola and Destin, you can try Navarre, FL, which is about half an hour east of Pensacola, or about half an hour west of Destin.
About ¼ or a fourth of the way, you can stop at Tiger Point, FL. This is about 18 minutes east of Pensacola.
About ⅓ or a third of the way, you can stop at Woodlawn Beach, FL. This is about half an hour east of Pensacola.
About ⅔ or two thirds of the way, you can stop at Wynnehaven Beach, FL. This is almost an hour east of Pensacola, or about half an hour west of Destin.
About ¾ or three fourths of the way, you can stop at Mary Esther, FL. This is almost an hour east of Pensacola, or about 18 minutes west of Destin.
If you drive straight through without stopping at all, the total distance is 48 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 1 hour, 11 minutes.