The good news is that you have a variety of options, Melissa! The hard part will be narrowing down your choices to the one restaurant that best fits your family's style. Here are my suggestions:
If your family is looking for a traditional turkey and all the fixin's type of meal, might I suggest
Liberty Tree Tavern at the Magic Kingdom? The menu offers comfort food favorites every day of the year, Christmas included.
If you opt instead for a culinary Christmas, you might consider
Artist Point at Disney's Wilderness Lodge. There, a sophisticated ambiance weaves together with a woodsy charm. Both the service and the food are practically guaranteed to be superb. The lobby of the resort--decorated for Christmas--alone is reason to book a reservation!
If you're looking to enjoy a low-key holiday, perhaps dinner at
'Ohana inside the Polynesian is called for. The meal will make you feel as though you're enjoying an island holiday, every bit as family-oriented as the one you'd have at home!