The best way to celebrate Christmas in Rome is by keeping Christ in Christmas. Most churches and basilicas will have church services on every day that you plan to be in Rome. That would include churches of other denominations other than Catholic (Anglican, Lutheran and Protestant).
Besides going to a church service, which would be open to all, even non-Catholics and non-Christians, you may wish to take advantage of the Urbi et Orbi Blessing of the Pope at Vatican City on Christmas Day. While attending Catholic religious services called the Mass, please keep in mind that only practicing Catholics in the state of grace may receive Holy Communion.
For practicing Catholics, the Urbi et Orbi Blessing is an occasion to obtain a plenary indulgence. For those actually in Rome, those attending the actual ceremony will have the opportunity to see the pope.
The Urbi et Orbi address and blessing are given each Easter and Christmas from the central loggia of Saint Peter's Basilica in Rome, at noontime, and are broadcast worldwide through the European Broadcasting Union and other linkups. The address concludes with greetings in many languages in relation to the feast celebrated.
The Roman Catholic Church grants a plenary indulgence by the willful grace and intent of the Pope, on the usual conditions, to those who "devoutly receive" the blessing that the Pope imparts Urbi et Orbi.
Since 1985, this indulgence is granted not only to the people in Saint Peter's Square, but also to those who though unable to be physically present, "piously follow" it by radio or television. - Urbi et Orbi (Wikipedia)
While in Rome one may chose to visit the Basilica of St. Maria Maggiore which for those who believe contains a relic of the Holy Crib of Jesus.
The Holy Crib
In the crypt under the high altar lies the celebrated relic known as the Holy Crib. A statue of Pope Pius IX kneeling before the ancient wooden pieces of the manger serves as an example to the faithful who come to see the first humble crib of the Savior. Pius IX's devotion to the Holy Crib led him to commission the crypt chapel, and his coat of arms is visible above the altar. The precious crystal urn trimmed in silver, through which the faithful can venerate the relic, was designed by Giuseppe Valadier. The Papal Basilica St. Maria Maggiore