I always like a really quiet New Years Eve with good food and drink. Having said that I would order room service. Kidani has some wonderful options and they allow you to order off the menu from Sanaa--one of the best restaurants at WDW. That, some great drinks and a movie and I'd be all set.
If you want to go out, I love Jiko (AKL), Artist Point (WL) and Grand Floridian Café. I also loooove the Hoop Dee Doo. But my first choice would be Sanaa room service!
You are doing exactly what I hope to do some day. It's a dream of mine to spend actual Christmas at WDW. I know it's busy, but we've been so many times that it's not about the attractions. I'd love to see Christmas eve festivities (at Kidani, Mickey and Minnie visit and they serve cookies and cider). I would love to wake up Christmas morning with my family at my favourite place on earth. Have a fabulous time and Merry Christmas!