Paul (and Jesus) based his calendar of activities on the biblical sabbaths and festivals. Acts states multiple times that it was Paul’s custom to worship in the synagogue on the Sabbath day, wherever he happened to be. (14:1; 17:2 etc.)
In Acts 20:6 it mentions that Paul sailed from Philippi after the Feast of Unleavened Bread, i.e. Passover. No doubt Paul had intended to be in Jerusalem for Passover in obedience to the command in Deuteronomy 16:16. We see in Acts 19:21 that Paul decided to go to Jerusalem, likely for Passover, but he was detained by events. In Acts 20:3 we see that “Because the Jews made a plot against him just as he was about to sail for Syria, he decided to go back through Macedonia”, putting him behind schedule.
A few days after this it mentions that he was in a hurry to reach Jerusalem before Pentecost (20:16), i.e. the Feast of Weeks, which was seven weeks after Passover. This was also one of the three feasts that Jewish men were to go to Jerusalem for. They had already missed the chance to get there for Passover.
Paul’s first epistle to the Corinthians also seems to be focussed on Passover. In closing the letter (16:8) Paul mentions that he plans to stay at Ephesus until Pentecost (the Feast of Weeks), which gives the impression that it is around Passover when he is writing. This impression is reinforced by his mentions of Passover in the body of the epistle. He uses it as an analogy in chapter five. “Your boasting is not good. Don’t you know that a little yeast works through the whole batch of dough? Get rid of the old yeast that you may be a new batch without yeast — as you really are. For Christ, our Passover lamb, has been sacrificed. Therefore let us keep the Festival, not with the old yeast, the yeast of malice and wickedness, but with bread without yeast, the bread of sincerity and truth.” (5:6-8) This analogy probably gets its effect from the fact that Passover is either about to happen or has just happened, so it is on people’s minds.
He also discusses the actual celebration of Passover at some length in chapter eleven. Since the Passover Seder includes quite a bit of liturgy before the meal is served, apparently some, probably Gentiles, are not waiting for the appropriate time, but are going ahead and eating right away. Paul rebukes them for this.
Another festival which is mentioned in passing to describe Paul’s itinerary is Yom Kippur, the Day of Atonement, which is only called “the Fast.” “Much time had been lost, and sailing had already become dangerous because by now it was after the Fast.” (Acts 27:9) We can see that Paul oriented his weekly and yearly schedules around the Sabbath and festivals that are commanded in the Torah.
Jesus also did the same. Luke 4:16 mentions that it was his custom to attend synagogue on the Sabbath. It is well known that Jesus’ final days before his death were the Passover season. He celebrated Passover with his disciples the night before he was arrested.
The gospel of John records other Passover occasions during Jesus’ ministry. In John 2:13 Jesus went to Jerusalem for a Passover early in his ministry. In John 6:4 it again says, “The Jewish Passover Feast was near.” And of course we’re all familiar with the Passover that Jesus celebrated with his parents when he was twelve years old. (Luke 2:41-50)
Jesus celebrated other of the biblical festivals as well. Almost the entire seventh chapter of John is devoted to Jesus’ activities at the Feast of Tabernacles (Sukkot) in the fall. In John 5:1 there is an unidentified “feast of the Jews” that Jesus goes to Jerusalem to celebrate. Jesus is even found in Jerusalem during Hanukkah, referred to as the Feast of Dedication in John 10:22.
Jesus and all of his followers in the New Testament were proponents of Judaism and observed the biblical festivals which God had commanded. There is no mention of anybody in the New Testament celebrating Christmas, Easter, or any of the “Christian” holidays. There is one mention of “Easter” in the King James translation, in Acts 12:4, but it’s a mistake. The Greek word is “pascha” which is a transliteration of the Hebrew “pesach”, which means Passover.
Jesus does seem to encourage combining the celebration of Passover with his passion and death. During his last Passover Seder with his disciples, he points out some of the symbolic elements of the Seder, the unleavened bread and the third cup of wine, and applies them to his flesh and his blood. Then he tells his disciples that every time they eat “this” bread (the Passover matzah) and drink “this” cup (the third cup of Passover), they should remember his death until he comes.
It’s such a shame that most “Christians” have abandoned the observance of the biblical festivals. There is no warrant in the New Testament to do so. And taking scripture as a whole, it seems that God would be pleased if those who claim to follow him would take seriously the celebrations that he established for his people.