If you're looking for a meeting place or a good stop around ½ or halfway between Destrehan and Boutte, you can try Dufresne, LA, which is about 6 minutes west of Destrehan, or about 6 minutes north of Boutte.
About ¼ or a fourth of the way, you can stop at Luling, LA. This is about 3 minutes southwest of Destrehan.
If you drive straight through without stopping at all, the total distance is 8 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 11 minutes.