Shel,
I'll resist the old joke about asking where to play golf in New Orleans and responding why would you want to play golf in New Orleans...well, I guess I didn't resist.
But, as someone who loves the city, Metairie is probably the best if you have access, although unlike many I did enjoy Pete Dye's TPC at New Orleans quite a bit for a flat course. Lots of strategy built in.
Audubon Park was cited in Tom Doak's CG as a creative use of limited acreage and it's an executive course in a public park with folks jogging and bicycling past with zoo sounds for ambience.
One cool place with a local vibe is the Joseph Bartholomew public course in Pontchartrain Park, named after the African American course architect responsible for many of the early New Orleans courses.
I haven't played the Reesified City Park course...not sure what they are calling it these days but I'm picturing long, hard, water, as I think they were vying for the tour tournament, replacing TPC.