Most of us today are tight for cash and it being New Years Eve today, babysitters are extremely scarce or out right extinct. Just because you are stuck at home instead of a night out does not mean that you can have fun in the celebration. Bringing in the New Year with the kids and you significant other can be a fun night, plus with the kids staying up that late, you'll get to sleep in New Years Day.
Since you are probably not the only ones that are making plans to stay home, call around and see what your friends and their kids are doing. Just because you aren't going out, doesn't mean that you guys have to spend it alone together. Some of my friends are even looking for someone to spend the night with that are also stuck with no money and nothing to so they can at least do it together. The more the merrier I say.
If you have cable, find some On Demand movies that the whole family will enjoy. They don't even have to be holiday oriented. When I was a teenager, and if you have teens at home, we always made it a horror movie night.