Hi Roberta,
Walt Disney World always has so much to do, and this is especially true during holidays. Since it is your first trip, you might be very happy simply taking in all that Walt Disney World has to offer even without the addition of special events for New Year's Eve and New Year's Day; however, if you are interested in ringing in the New Year Disney-style, there are many special events occurring.
There are
events at Magic Kingdom, Epcot, and Disney's Hollywood Studios on New Year's Eve 2013. At Epcot, you can enjoy celebrations through different cultures with bands and DJs around World Showcase. At Disney's Hollywood Studios, enjoy the energetic music of Mulch, Sweat, and Shears. Magic Kingdom, Epcot, and Disney's Hollywood Studios will all have amazing fireworks displays on New Year's Eve. All of these shows will be amazing, but please do note - the theme parks will be very crowded. Consider getting to the theme parks pretty early on New Year's Eve to ensure your spot. An alternative event at Downtown Disney is the
New Year's Eve Party at DisneyQuest Indoor Interactive Theme Park.
My fellow Disney Parks Moms Panelist Kimberly L. recently wrote a great article on things to do at Walt Disney World on New Year's Eve. You can find it at the unofficial site disneyfoodblog.com. Go to that site and search "New Year's 2013" and it will be the first link. This article includes information on dining on New Year's Eve as well. I suggest that you treat New Year's Day like any other day at Walt Disney World. Choose the theme park that you would like to go to, arrive early since it will likely be crowded, and enjoy your day!
Please do not hesitate to ask if you have any further questions, Roberta!