For the last day I have been hunting down a description of the Serapeum in Alexandria. I learned of it from Philip Amidon’s translation of Rufinus. The description is recorded — of all places — in the handbook of rhetoric by Aphthonius of Antioch. This writer was a friend of Libanius, and lived in the late fourth century.
The description is there, not for its content, but rather as an example of a relaxed style (!). It has been no mean hunt to locate the materials, but in fact a complete translation of the text is available from Malcolm Heath here, and here. The word “Serapis” does not appear in the text — on the face of it, the description is of the acropolis. But in fact it is the Serapeum.
A text in Greek is available in Rhetores Graeci, vol. 2, 1854, p.47-49. The 1926 Teubner by Hugo Rabe, with the commentary of the 9th century John of Sardis (compiling much earlier information), does not seem to be online.
Rather than quote the Heath translation, here is the translation by George Kennedy, who has translated and annotated four rhetorical handbooks, and some of John of Sardis. The Google books preview only gives the opening bit. Page numbers in Rabe are marked with R, the other numbers in  are from the Rhetores Graeci text, whose page numbers have become standard.
ECPHRASIS OF THE SHRINE OF ALEXANDRIA, WITH ITS ACROPOLIS
Citadels, then,87 have been built in cities for the common security; for they are the highest points in the cities, and they are not themselves more fortified with buildings than they fortify their cities. The middle of Athens has embraced the acropolis of the Athenians, and Alexander had a height prepared in his own city, constructed to suit the name he gave it;88 for he set it on the highest point of the city, and it is more sensible to call it an acropolis than that on which the Athenians took counsel.89 Its appearance is as this account will describe.
An ”akra” projects up from the land, going up to a considerable height, and is called an “acropolis” for two reasons: because it is raised to a height and because it has been set on the high point of a city. Roads leading to this acropolis are not alike; for here there is an incline (”anodos”) and there an entrance way (”eisodos”). The roads change their names, being called by their function: here it is possible to go on foot and the way is public and a road for those going by carriage; on another side, flights of steps have been constructed [39R] where it is not possible for carriages to go. Flight of steps follows flight of step, always increasing from the lesser and leading upward, not ceasing until there have been a hundred steps; for the limit of a number is the end  that reaches perfect measure.90
At the top of the stairs is a Propylaeon, enclosed by latticed gates of moderate height, and four very large columns rise up, providing several openings into one entrance passage. Above the columns stands the Oecus, fronted by many smaller columns which are not all of the same color, and when compared they add ornament to the design. The roof of the building rises in a dome, and around the dome is fixed a great memorial of things that are.91
On going into the acropolis itself, one enters a single open space, bounded by four equal sides, and its figure is rather like that of a war machine (i.e., a hollow rectangle). In the middle is a courtyard, surrounded by a colonnade. Stoas continue the courtyard and the stoas are divided by equal columns, and as for their measure, it is the largest possible. Each stoa ends [40R] in another crosswise colonnade and a double column divides it from another stoa, one ending and the other beginning again. Small covered structures are built inside the stoas; some are reading rooms for books, offering an opportunity for the studious to pursue knowledge and arousing the whole city to the possibility of wisdom; others were built as shrines to the ancient gods. Gold adorns the roof of the stoas and the capitals of the columns are made of bronze, overlaid with gold. The decoration of the courtyard is not all the same; different parts were done differently. One part has a representation of the contests of Perseus. A column higher than the others stands in the middle, making the place conspicuous.92 A visitor, up to this point, does not …
87 Unlike the other examples of composition, this begins with connective particles (”de ara”), contributing to the relaxed style; see John of Sardis’ commentary on this ecphrasis, translated below.
88 I.e.. the name “acropolis,” but the sentence is clumsy and possibly the text is corrupt. Alexander’s city is of course Alexandria.
89 The Areopagus?
90 “In its completed form the plateau on which the Temple stood was approached from the north and south sides by a carriage road and from the east side by a flight of 200 steps,” John Marlowe, The Golden Age of Alexandria (London: Victor Gollancz, 1971). p. 60. For more information about the Serapeum, see I. A. Rowe, “Discoveries of the Famous Temple and Enclosure of Sarapis at Alexandria”, Annales du Service de l’Antiquite de l’Egypte, Cahier supplementaire 2 (1946).
91 “At the top of the steps was a Propylaeum supported by four large columns and approached between two obelisks. Immediately inside the Propylaeum was an Oecus, or circular hall, covered by a gilded dome resting on a double ring of columns,” Marlow ibid. The “great memorial of things that are” was probably a religious and historical fresco.
92 This monument, some 80 feet high, was known as “Pompey’s Pillar,” but was actually erected to commemorate a visit to Alexandria by Diocletian in A.D. 297, when he suppressed a revolt.
Unfortunately the Google Books preview breaks off there.
Doesn’t that translation seem good! Of course the Heath translation was made earlier, and is merely a rough draft. Here is the remainder of the entry, from Heath:
…. where he is going, unless he uses the pillar as a sign of the direction) and makes the acropolis stand out by land and sea. The beginnings of the universe stand round the capital of the column. Before one comes to the middle of the court there is set an edifice with many entrances, which are named after the ancient gods; and two stone obelisks rise up, and a fountain better than that of the Peisistratids. And the marvel had an incredible number of builders. As one was not sufficient for the making, builders of the whole acropolis were appointed to the number of twelve.
As one comes down from the acropolis, here is a flat place resembling a race-course, which is what the place is called; and here there is another of similar shape, but not equal in size.
The beauty is unspeakable. If anything has been omitted, it has been bracketed by amazement; what it was not possible to describe has been omitted.
Who would have thought that so obscure a writer was nevertheless online in several Greek versions, older Latin translations, and two English versions? Truly we live in a blessed age!
UPDATE: My thanks to Domenico in the comments for pointing out my mis-spelling of Aphthonius as Apthonius. Aargh!