Hi tazio1976, welcome to CruiseReviews. I LOVE cruising at Christmas because it reminds me of Christmas when I was a young girl. I grew up in Ft. Lauderdale, so palm trees, and warm weather are the way to go for me
I hope you enjoy NCL as much as we do. I've sailed them 6 times and have always had a great time. The ports you are visiting are great, too!
I don't know what activities you enjoy, but if snorkeling is one of them, Costa Maya, Belize or Roatan are fantastic for snorkeling. Cozumel is nice, too, but the reef in Costa Maya, Belize, and Roatan is second only to the Great Barrier Reef. Crystal clear water in all of the ports, too.
Tulum ruins in Cozumel will take you about 2 1/2 hours travel time, round trip. However, the ruins and setting is spectacular. Nadine's suggestion is probably the best, as the travel time is not as long. You could save Tulum for your next cruise when you stop at Playa Del Carmen or perhaps Progresso. Notice, I already have you cruising again, because I'm betting you'll be hooked like the rest of us.
Hope you have a marvelous time, perfect weather, and enjoy the Spirit! My coworker sailed out of New Orleans all the time. He said it's an easy port to get into/out of. He parks at the port as he drives down from Huntsville, Alabama.
One suggestion I have, is whether flying or driving, come in at least a day early so you will not have stress before your cruise. I doubt the weather will be too bad in Arkansas, but you never know. But, if you come in at least the day before, you can be relaxed and not pushing to get there. And, New Orleans is a fun city to visit.