There are some amazing musicians in New Orleans, also some very good engineers and producers. But most studios are a bit smaller or more limited than what you're looking for.
Nevertheless, here are a few places that are doing good work:
1) Studio In The Country - just outside the city in Bogalusa. Studio In The Country
2) The Music Shed - The Music Shed Recording Studios - New Orleans, Louisiana
3) Axistudio - axistudio
4) Fudge Recording Studio - fudgerecordingstudio
Good luck and hope you enjoy your time in the city!