If you're looking for a meeting place or a good stop around ½ or halfway between New Orleans and Pensacola, you can try Pascagoula, MS, which is about 1½ hours east of New Orleans, or about 1½ hours west of Pensacola.
About ¼ or a fourth of the way, you can stop at Bay Saint Louis, MS. This is almost an hour northeast of New Orleans.
About ⅓ or a third of the way, you can stop at Gulfport, MS. This is almost an hour northeast of New Orleans.
About ⅔ or two thirds of the way, you can stop at Mobile, AL. This is about 2 hours northeast of New Orleans, or about 1 hour west of Pensacola.
About ¾ or three fourths of the way, you can stop at Daphne, AL. This is a little over 2 hours east of New Orleans, or about half an hour west of Pensacola.
If you drive straight through without stopping at all, the total distance is 201 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, 56 minutes.