Hi Steve,
Thank you so much for visiting the Disney Parks Moms Panel with your question. We on the panel love helping guests to plan magical vacations!
I visited Walt Disney World with my family over New Year's Eve a few years ago, and we had a wonderful time. There is so much to do at
Walt Disney World on New Year's Eve! I like your choice of Epcot as the place to be on this holiday; it is one of my favorite theme parks. I have good news for you. For entrance to the park and to be in the theme park, you just need your regular Disney theme park admission.
There are many options for
dining at Epcot. As you mention, you could simply stop at quick service dining locations or kiosks around Epcot. I suspect that it will be fairly busy that night so you should prepare for some waits if you decide to do this. If there is somewhere that you really would like to have a sit down meal, I suggest that you check to see if you can make a reservation. This might be difficult to get this close to the date, but it is always worth a try. You never know when another guest is going to cancel a reservation! Another possibility is the New Year's Eve Dinner at the World Showplace Pavilion. There is more information on this from the first site that I linked. It includes a delicious holiday buffet. To make reservations for this or any other Walt Disney World dining experience, you can call 407-WDW-DINE (407-939-3463). If you want to make reservations at a table service restaurant, you can do this from the dining at Epcot link I provided earlier.
I hope that these thoughts are helpful for you, Steve! Have a wonderful time celebrating at Epcot!