I know NOCC well, too well.
The two most prestigious country clubs in NOLA are the New Orleans Country Club and Metairie Country Club. Both are very fine clubs with golf, tennis, swimming and terrific party facilities as well as distinguished and engaging members.
The best feature of both clubs are the parties. The biggest handicap both clubs have to deal with regarding golf is the land. It is flat, flat, flat.
Metairie is originally a Seth Raynor design and has been renovated recently. I have not played the course since their renovations but have seen some pictures that suggest it was a pretty stellar job. The New Orleans Country Club was last renovated (I am not exactly sure) but I want to say in the late 1980's early 1990's. It is a moundy affair with live oaks providing some strategic problems. The climate in NOLA is not favorable for fast greens so be prepared to thump those putts.
I am most familiar with NOCC and in my opinion it is just OK. Nothing really to write home about. I would very much like to play Metairie again to see how the renovations went first hand.
Katrina submerged both properties under at least 10 feet of water. The first floor of NOCC was ruined but is now restored. Metairie ended up demolishing the old clubhouse, not a great loss in my opinion, and building a very nice brand new one.
My two cents. Try Metairie. Otherwise enjoy NOLA for what it truly excels at, Great Parties, Great Food, Great People!