Craig,
I'm going to go out on a limb here, meaning no affront to the fine fellas from Louisiana who participate here.
Since it seems that there really aren't any excellent modern courses in New Orleans (I played Landmark's Belle Terre about 35 minutes west of NO, and although it is designed by Dye associate David Pfaff, it's maybe a 4), then I suggest you imbue yourself with some of the local history and color.
I suggest instead that you head directly to the Bayou Oaks Golf Course, which was formerly known as City Park GC.
Ask to play the "Wisner Course", and if you have time, also play the more difficult "Championship Course", but only as the second choice.
What will you find on the Wisner? History, my friend.
Consider...
The Wisner Course contains the considerable remants of the original City Park course #2 that hosted the New Orleans Open, which was one of Byron Nelson's 11-in-a-row streak in the 40s.
The Wisner Course has by far the most interesting green complexes of the 4 courses at Bayou Oaks.
The Wisner Course was originally designed by a black man...Joe Bartholemew...who was a Raynor disciple forbidden from ever playing a course that he designed. See the book "Forbidden Fairways". A fellow named Richard Koch had some hand, as well, but Bartholemew was the main guy. Incidentally, the Championship course is a Ralph Plummer affair from 1968, and it's tougher but not as interesting.
The Wisner course costs probably the princely sum of 20 bucks or so to play.
You're likely to join up with some locals there, and that's worth the price of admission in any case.