Disney's Hollywood Studios would be a wonderful place to spend New Year's Eve; however, DHS is most definitely NOT the only park that will be hopping on that night.
If you look at the park calendars found
HERE, you'll see that three of the parks are open extra late on December 31. Additionally, the Magic Kingdom is having Fantasy in the Sky Fireworks at 11:50 (a great way to ring in the New Year) and Epcot is having a special showing of Illuminations at 11:40. Also, restaurants all over WDW will be offering special New Years menus.
Both DHS and Epcot will be less crowded than the Magic Kingdom, which will have a crush to rival Times Square. If crowds are an issue for you, I'd stay at Epcot where the large park will give you more square footage per person. But regardless of where you decide to spending the evening, you can be sure that guests at WDW will be out celebrating.
Have a great trip!