My partner and I love to go to the park for New Years! It is extremely crowded on New Year's Eve (probably the most crowded you will ever see the park) and we always make sure to get in line outside the gates with pleanty of time to spare before opening. They can close the park due to capacity by 10AM...
And, once inside on New Year's Eve, you need to just relax. With your 3 other days, plan on sort of kissing off NYE as far as rides go because the lines will be rediculous. But, there is still plenty of other magic to enjoy in the park. I like sitting on the balcony outside the Disney Gallery and watching all the crowds go by. Then, around dinner time, head over to the hub and stake out your place right in front of the castle. The NYE nighttime shows are fantastic fun. Several fireworks displays, live singers, tons of Mickey appearances, and usually huge beach balls to bat around above the crowd! The hub turns into Times Square as it gets dark, and it gets almost impossible to move. So running to get food or bathroom breaks takes longer than normal.
Also, if you get a chance, they usually have small stages and parties set up all over the park. The stage back by It's a Small World is usually a lot of fun.
Then, the best news of all! New Year's Day, the park is dead! It is such a breath of fresh air to be able to go on every ride you want to after such a stressful day of crowds. Enjoy Jan. 1, and good luck. Feel free to private message me if you have any specific questions because I've done New Years several times.