P.F.
We love a family NYE - we usually make it a game night too, and have over another family who can either walk home or stay the night. We toast the NY at 9pm with the kids (watching the live ball drop) and bang pots and pans on the back deck.
Re the next day, we also try to spend that day as we want to spend the new year. One idea, depending on your kids' ages, is to make a garland of hopes. Just like the paper garlands we made for xmas as kids, you take single strips of paper. Write on it a dream/hope/resolution and then make a link out of it....put all the family dreams together to form a garland that you can string up for a while and then put away to review next year or mid-year. We do it at Christmas with the names of people we love and are thinking about.