L.M.
Board games, perhaps? Let them have a dance party? Offer them a place to play "grown ups" and have 7-up or punch with cherries and umbrellas and some music. Or make it a theme and make sure they have some of the traditional new year's eve accouterments like Hawaiian leis and party hats, etc... Ask one of the older kids to be the "DJ", they'll enjoy the "responsibility". Encourage them to play musical chairs or other music-based games that all the kids in that age range can play. Duck-duck goose is good for getting energy out and all you need is a little room for them to sit in a circle and run around each other. If you've got the room (preferably a basement), get a pinata and let them whack at that later in the evening.
<a href=http://www.imdb.com/title/tt0073640/>Rudolph's Shiny New Year</a> is always a good video for kids in the 5-10 year old range. It's a classic and kids always seem to enjoy it.
I guess in general I don't worry about kids being bored; they will figure out something to do, they don't need everything choreographed and don't need to be entertained. As children we just "figured out something to do" when the adults got together. No one entertained us/scheduled activities and we always had a blast. I'm of the opinion that we don't let children just play unstructured enough, so they don't learn to entertain themselves/play together/organize games themselves so I tend to not organize things for them but rather give them the tools to do so and let them play. They'll figure it out and enjoy themselves because they hate being bored more than we do.