If you're looking for a meeting place or a good stop around ½ or halfway between New Orleans and Montgomery, you can try Prichard, AL, which is a little over 2 hours northeast of New Orleans, or a little over 2 hours southwest of Montgomery.
Other possible places to stop near the midpoint include Saraland, and Eastwood.
About ¼ or a fourth of the way, you can stop at Biloxi, MS. This is a little over 1 hour northeast of New Orleans.
About ⅓ or a third of the way, you can stop at Pascagoula, MS. This is about 1½ hours east of New Orleans.
About ⅔ or two thirds of the way, you can stop at Canoe, AL. This is almost 3 hours northeast of New Orleans, or about 1½ hours southwest of Montgomery.
About ¾ or three fourths of the way, you can stop at Evergreen, AL. This is a little over 3 hours northeast of New Orleans, or a little over 1 hour southwest of Montgomery.
If you drive straight through without stopping at all, the total distance is 309 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 4 hours, 23 minutes.