Hi splean, there is nothing long distance of note within an hours drive on NOLA. There are a few indoor pistol ranges the better being in Metairie. For outdoor ranges, there is a 100 yard outdoor range on a wildlife management area named Pearl River; that one is about an hour or so north of NOLA and it is $8 to shoot all day.
There is Palo Alto in Donaldsonville, LA but that is membership only; $250 for 1st year membership and application fee. That one goes out to $600; I have never gone there.
About 30 minutes past Pearl River there are a few rifle ranges that I have been interested in going to. They are in Mississippi and are pretty much along the coastline.
I am still learning and in the process of getting my gear setup but if you want to meet we can go check one of them out.