Hello Carey,
Spending New Year's Eve at Disney World has always been a dream of mine. Sounds like your family is in for a magical time!
Once you've battled the holiday crowds, most guests leave after the first or second of the year. After that, I have heard crowd levels dwindle, and you will feel like you virtually have the parks all to yourself.
California Grill is a wonderful spot for dinner. The food is magnificent, and the views are breathtaking. And if you time your reservations just right, you can watch Wishes, the Magic Kingdom fireworks show, from inside the restaurant or from the outdoor Observation Deck.
But as first time visitors, may I suggest another restaurant located at the Contemporary Resort:
Chef Mickey's. Everyone in your family will enjoy seeing Mickey and all his pals. And as a parent, I'm always grateful to be able to find my daughter's favorite characters all in one spot, at one time!
No matter where you choose, I hope you and your family have a memorable vacation! Enjoy your trip!