We spent 12/31 2000, and 1231/2001 at Disneyworld. Both trips we arrived on about 12/29 and stayed through 1/01. The first year we spent at MGM. The second year at Epcot. Both times, the parks filled up by about 11am and no one else was admitted. This would also prevent you from leaving. We had a great time at MGM, but after that experience, our Epcot New Year's Eve went a little more smoothly. The biggest advice I have is to plan your day around your meals. We arrived in Epcot at 8:45. Just as a point of reference, the Test Track Fast Pass was already out to 3pm. We had made ps for Garden Grille for lunch. This is a great place to "chill out" in the middle of the day. We love this restaurant for the atmosphere and the food. It was really nice to take a long lunch break while revolving around The Land. We then spent the afternoon walking around the world showcase. It was really crowded, but most everyone was festive. We had ps for dinner at the Rose and Crown for 7pm. This happens to be midnight in England, so we celebrated early! Keep in mind, that all the countrys celebrate the New Year at the appropriate time if you choose Epcot.
To wrap up, pick a park and make priorty seatings for maximum rest times. Have fun!!!!