New Years is a family event so there are not many tours or much excitement surrounding the new year like there is in the US. My family makes mochi and then we head to Kiyoshikojin Temple (http://www.kiyoshikojin.or.jp/en/) for hatsumode (first temple visit of the year) early in the morning.
Some ryokans serve special meals over the new years though prices are generally higher than normal and you must book early. Many smaller ryokans close so the workers can spend time with their families.
My advice is to head to a local temple and just soak it all in.