December 31, Seventh Day in the Octave of Christmas
The last day of the year is also the feast of St. Sylvester bishop of Rome in 314. Constantine gave him the Lateran Palace, which became the cathedral church of Rome. Many legends exist about Sylvester. He supposedly cured Constantine from leprosy and later baptized him on his deathbed.
New Year's Eve, along with its innocent gaiety, is really a day for serious reflection. On the eve of the civil New Year the children may join their parents in a holy hour, in prayer and thanksgiving for the gifts and benefits which God has given them in the past year, and to pray for necessary graces in the forthcoming civil year.
January 1, Solemnity of Mary, Mother of God
Although New Year's Day is not celebrated by the Church, this day has been observed as a holy day of obligation since early times due to the Solemnity of Mary, Mother of God. Each family and country has different traditional foods to eat on New Year's Day, with lentils being the main superstition: ill luck befalling those who do not eat lentils at the beginning of the year.
New Year's is a day of traditional hospitality, visiting and good cheer, mostly with a secular view, but there is no reason that this day, too, could not be sanctified in Christ.