Disney is my favorite place to enjoy the New Year. Planning on heading back this year. The Magic Kingdom treats both 12/30 and 12/31 as NYE, and so many people do MK on the 30th, and Epcot on the 31st. Both parks are magical and completely different than any other time in the year as they approach the new year, with special entertainment, usually 2 firework shows that evening, special pyrotechnic finales to welcome the new year, and DJs. Epcot tends to handle the crowds a bit better on the 31st as well.
The Magic Kingdom's fireworks are also presented in full 360 for the finale, and it's absolutely beautiful.
As the previous poster said, be flexible, prepare for insane crowds and wait times, ARRIVE EARLY TO THE MAGIC KINGDOM (it will close around 10-11am), traffic will be TERRIBLE, the parking lots are a free for all, but it's one of the most amazing experiences at the World. Take it laid back, and don't expect to rush anywhere, and it will be an incredible experience.