Thomas Taylor, the 18th century translator known as the “English Platonist”. wrote a two volume translation of 41 dissertations by Maximus of Tyre, in which there is material from Libanius about pagan festivals. The material is in vol. 2, p.267, and belongs to the Descriptions, part of the Progymnasmata.
Whether the festivals described are based on Antioch, or Athens, is not clear. I suspect that they are not likely to be Constantinople. Could this be a reflection of the rites at the Temple of Apollo at Daphne?
"Solemn festivals when approaching produce desire in the human race, when present they are attended with pleasure, and when past with recollection : for remembrance places men very near the transactions themselves. The recollection also possesses a certain advantage. For in speaking of solemn festivals it is also necessary to speak concerning the gods in whose honour they are instituted. Men prepare themselves for these festivals when they approach with joy. The multitude, indeed, procure such things as may furnish them with a splendid entertainment, but the worthy those things by which they may reverence the gods. Cattle and wine, and whatever else is the produce of the fields, are brought from the country. Garments also are purified ; and every one is anxious to celebrate the festival in perfection. Those that are in want of garments are permitted to borrow such as are requisite to adorn themselves on this occasion from those that have abundance. When the appointed day arrives the priests open the temples, pay diligent attention to the statues; and nothing is neglected which contributes to the public convenience. The cities too are crowded with a conflux of the neighbouring inhabitants, assembled to celebrate the festival; some coming on foot, and others in ships.
At sun-rise they enter the temples in splendid garments, worshipping that divinity to whom the festival is sacred. Every master of a house, therefore, precedes bearing frankincense : a servant follows him carrying a victim ; and children walk by the side of their parents, some very young, and others of a more advanced age, already perceiving the strong influence of the gods. One having performed his sacrifice departs ; another approaches to perform it. Numerous prayers are everywhere poured forth, and words of good omen are mutually spoken. With respect to the women, some offer sacrifices in the temples, and others are satisfied with beholding the crowd of those that sacrifice. When such things as pertain to the divinities are properly accomplished, the tables follow, at which hymns are sung in praise of the god who is honoured in the festival. Social drinking succeeds, with songs, which are partly serious and partly jocose, according to the different dispositions of the company. Some, likewise, feast in the temples, and others at home; and citizens request strangers to partake with them of the banquet. In the course of drinking, ancient friendships are rendered more firm, and others receive their commencement. After they have feasted, rising from table, some take the strangers, and show them whatever is worthy to be seen in the city, and others sitting in the forum gaily converse. No one is sorrowful, but every countenance is relaxed with joy. The exaction of debts gives place to festivity, and whatever might cause affliction is deferred to another time. Accusations are silent, and the judge does not pass sentence ; but such things as produce pleasure alone flourish. The slave is not afraid of blows from his master, and pedagogues are mild to youth.
In the evening they sup splendidly, at which time there are so many torches that the city is full of light. There are also many revellers, and various flutes, and the sound of pipes is heard in the narrow streets, accompanied with sometimes the same, and sometimes different songs. Then to drink even to intoxication is not perfectly disgraceful ; for the occasion in a certain respect appears to take away the opprobrium. On the following day the divinity is not neglected ; but many of those that worshipped on the preceding day do not again come to the shows. Those that contend in the composition of verses attend on this, but those with whom the contest is in the scenes on the preceding day. The third day also is not far short of these; and pleasure and hilarity are extended with the time of the festival. When the solemnity ends, prayers are offered for futurity, that they, their children, and families, may again be spectators of it ; after which the strangers depart, and the citizens accompany them".