Just about every restaurant in town will have special new Year's eve dinner offerings. You don't mention a price or preference. Since you'll be at Boubon St., you'll probably want to stay on Duval. For a great meal, try 915 (it's right on Duval) but you should hurry, they might already be booked.
OR, for tapas and good wine, try Santiago's Bodega in Bahama Village, that's also fairly close but, again, it's so close to the date that they might be booked.
Good luck and Happy New Year.