J.F.
Typically we do our own New Year's Party. We invite our friends and family to our house, kids are completely welcome. We have a bonfire, make smores, my dad is a dj partime, so he sets up the sound equipment and we play dance music, we all dance in the yard, play games, adult's can drink, as long as they don't get trashed and take enough time away from it, to sober up, or they stay with us for the night! We do fireworks and sparklers, we make finger foods and special cookies and cakes, everyone brings something to drink(that even little ones can drink) and eat and we just spend the whole night laughing and getting together with our friends. My son is only 18 mnths old, but we've been doing this since I was 14. We used to do it at my parents house, but we now do it at my house, since I have more property. We pull the 4-wheelers out and the older kids and grown-up kids(ie my husband!) go to the other side of the property or the woods and ride around.
Just make it your own. Invite your family and friends, and your children's friends over, and just make a night of it! It's the one night that I think they should be able to stay up and watch the ball drop! Get some sparkling grape juice and let them toast to the new year. Aske them what their goals are for the new year and find out what they are wanting to accomplish that year! It'll be fun, you'll see. And that's something that your children will carry on, when they have kids of their own...I did!