Played TPC, English Turn and Audobon in the summer on a guys trip. TPC is the nicest of them all, but also the priciest. I was fairly surprised by English Turn since most of what I had read said the course had gone downhill, but I thought it was in good shape and pretty fun. Both of these are not close to where y'all are most likely gonna stay if that matters (I'm assuming near the French Quarter). Audobon park is par 3ish type course close to heart of New Orleans. Not particularly nice, but still fun.
You can't go wrong with TPC if money isn't a problem.