Hi Tammie!
Spending a holiday at Walt Disney World is always special and fun but you will also encounter the largest crowds. Since you will be staying at the beautiful
Grand Floridian Resort my suggestion is to stay close by for New Years Eve to make it easy for yourselves. None of the Disney resorts will have actual celebrations at midnight as you can only imagine how that might interfere with the guests who are choosing to head to bed at their normal time. But the
Magic Kingdom theme park is only steps away and that is where a huge celebration will take place that evening.
You can easily head to the park to watch the grand fireworks or find a place at your resort to watch and make a midnight toast. I spent New Years Eve at Walt Disney World in 1999/2000 and will always remember how special it was.
Once New Years passes the crowds will diminish and you can head to the parks with more ease. Although Walt Disney World is never quiet anymore it will be a week of shorter lines and people in the parks. The marathon crowds will descend next and they come in great numbers for this yearly race weekend. It will be important that you keep up with the resort information about road and park closings. Disney tries to make all guests happy but this big weekend will alter some of the plans you might regularly make.
If you have the choice I do recommend coming to Walt Disney World once the marathon weekend has passed. January is generally a slower month up until Martin Luther Kings weekend. That can be a busier weekend with many of the local Floridian coming for a visit. Crowds will again drop down after that until Presidents weekend mid February.
Whatever time you can plan a visit you will simply make it work!