I get to NOLA frequently as my wife is a native, (Academy of the Sacred Heart girl).
My GF is a Domincan girl.
Metairie is a great old Raynor course. All the template holes. Not much going on that piece of ground, but a wonderful membership and a fun round of golf. Don't miss the Grillades and Grits!
I think Audubon Park is the most interesting golf experience in town. Not much of the John Bartholomew bones remain, BUT they do celebrate him and his legacy. The clubhouse is fantastic, set amid beautiful live oaks. And if you're serious about the future of golf (and Adam, I know you are) then it's very interesting to see this 4200-yard, par 62 track. It's in great condition, and you can get it around pretty quickly at Audubon, which leaves more time for NOLA. I was there the day it reopened following Katrina (this would have been after Christmas, 2005). Grown men were crying like babies.
Other than that, check out the Ron Garl re-design of Lakewood CC, on the West Bank. Lakewood hosted the PGA Tour for 26 years. The course is now owned by the New Orleans Fireman's Pension Fund. Some people like English Turn. I don't.
In terms of good NOLA culture, spend an afternoon walking up and Magazine Street. More of a local spot than the Quarter or even St. Charles Ave. Stop in at Octavia Books - one of my favorite bookstores in the world. I think Guy's Po-Boys are the best in town (the beef w/ debris is out of hand good). Lots of cool shops and stops as you work your way up Magazine from the Audubon Park side toward downtown.
Grab some crawfish at Frankie & Johnny's while you're in the area.
In terms of a premier dining experience, it's Galatoire's all the way. By a mile. Commander's is good but not great, IMO. Court of Two Sisters is good but not great. Muriel's is really good. But Galatoire's is GREAT. Lunch is also a good time to head in and get a good table for one of the best culinary experiences in America. The Crab Yvonne is unbelievable, and so is the Redfish. Modern restaurant: Jacque-Imo's on Oak Street.
Oysters = Felix's or Acme Oyster House. For good jambalaya, gumbo and other "down home" cookin', I like Mother's on Poydras. My GF prefers Mandina's on Canal. Both are killer, although you certainly pay a destination tax on either of them.
Music: Tipatina's on Tchopitoulas, Maple Leaf, Rock and Bowl. Insider's special - Le Bon Temps Roule (Magazine St). Smoky, sweaty little room. Incredible unannounced late-night appearances.
Did I mention that I LOVE New Orleans?