Was their tourism or pilgrimage from Alexandria and other parts? Were there conservation efforts and reverence for the past? I know Cleopatra ruled from Alexandria, and was also wondering if there's any evidence that she visited the great pyramids at Giza and what type of ceremonies if any would she have attended at the site? Would she have been recognised by the priesthood as the successor of the great pharaos? Or was there no priesthood there by that time?
More importantly, would they (the priests, the scholars of her time) have known what the pyramids were built for originally? Was Cleopatra aware they were burial monuments and would she have known who was buried there? Or would they have thought they were ancient temples, perhaps built by the gods? Did they find them perhaps mysterious and inscrutable, as they did not have access to archaeology? Or alternatively, was oral and written tradition stable, strong and continuous in a way that they would have known even much more than we do, although thousands of years had passed? What do the historians of her time tell us about these ancient monuments, if not Egyptian historians then at least Roman and Greek ones?
The Roman tourist squinted.
The afternoon sun was bright - it seemed to always be bright in Egypt- and the pyramid's sides shone with painful intensity. The climbers, now almost to the top, were specks in a quivering expanse of white. Shadowing his eyes with his hands, the tourist tried to guess the route they would take to the top. He had heard, of course, that the villagers of Busiris would climb the pyramid for a fee, but actually seeing the men work their way up the face, following long cracks and fingerholds invisible from the ground - well, he would have paid much more than a few tetradrachms to see that. His guide pointed. "Look!" The first climber was on point of reaching the pyramid's top...
By Cleopatra's time, the Pyramids of Giza were famous far beyond Egypt, and were highlights of a well-established tourist circuit. They still had most of their casing stones - those would be stripped after being loosened by medieval earthquakes - though they appear to have been in less than pristine shape by the first century CE, when wealthy tourists like the imaginary Roman of our opening anecdote paid villagers to climb to the top, presumably using the cracks between shifted blocks.^(1) In time-honored fashion, quite a few Greek and Roman tourists left graffiti on the lower courses; early modern tourists recorded - among other inscriptions - a poignant Latin poem written by a Roman woman lamenting her brother.
As for Cleopatra in particular, it is all but certain that she visited, most famously when she voyaged up the Nile with Caesar and a flotilla of 400 boats.^(2) There is no explicit mention of her stopping to admire the pyramids, but it would have been surprising if she did not. The Egyptian priesthood was still a vibrant force in her time, as it would be for centuries. But as I've discussed in an older answer, there was a surprising amount of uncertainty about the age and original purpose of the Giza pyramids.
Greek and Roman authors knew that the pyramids were tombs, but tended to assume that they were much younger than the actually were. To quote my older answer, which focuses on the Great Pyramid:
Herodotus, the father of history, devotes the second book of his Histories to Egypt. His sources (he claims) were Egyptian priests - but since he was forced to communicate with them through an interpreter (and acquired a great deal of hearsay from other sources), his narrative often presents a rather garbled version of Egyptian tradition. Herodotus came to understand the depth of Egyptian history.^(3) His account of the Great Pyramid, however, is chronologically displaced: he makes Cheops (Khufu), the pharaoh who built it, the grandson of a man whom he describes as a contemporary of Helen of Troy - that is "about 800 years before my time [c. 430 BCE]."^(4)
Diodorus Siculis (a Greek historian who wrote in the first century BCE) presents a detailed account of ancient Egypt in his first book. Like Herodotus, he was aware of (and in fact exaggerates) the depth of Egyptian history.^(5) Again like Herodotus, he dates Khufu to shortly after the time of Trojan War.^(6) He actually makes Khufu even more recent than Herodotus, describing him as having reigned nine generations (i.e., almost three centuries) after Proteus.
The Greek geographer Strabo, also working in the first century BCE, describes the Pyramids at Giza, but provides only vague details about their dating. The Pyramid of Menkaure he calls the "Tomb of the Courtesan," and associates with a woman named "Doricha, the beloved of Sappho's brother Charaxus."^(7) Since the poetess Sappho flourished in the late seventh century BCE, Strabo thus radically underestimated the date of at least this pyramid.
In his compendious Natural History (a sort of encyclopedia), Pliny the Elder (first century CE) briefly discusses the Great Pyramid. But he doesn't know how old it is, and frankly doesn't much care. In fact, he isn't even sure who built it.^(8) Pliny also repeats the story about the Pyramid of Menkaure being dedicated to a courtesan - in his account Rhodopis, a fellow-slave of the Aesop (traditionally said to have flourished in the early sixth century BCE).
Why were these Greeks and Roman authors so misguided? They were certainly in a position to know better - Manetho, a Greek-speaking Egyptian priest, had composed a relatively accurate chronology of the Egyptian pharaohs' reigns in the third century BCE; and the many wealthy Romans who visited Egypt could have consulted with learned Egyptians during their tours.
There seem to be two sources of misinformation in the sources quoted here. First, Herodotus, whose work was a widely-read "classic" by the Roman era, had established an account of Egypt that some authors (and especially those who never visited Egypt themselves) regarded as definitive; Herodotus and other members of the literary tradition he established were simply imitated. Second, and I think more importantly, the Greeks and Romans (but especially the Greeks) had a habit of explaining every other culture's history and norms with reference to their own. Fitting Khufu (as Cheops or Chemnis or some other name) into a familiar Greek chronology as the descendant of a figure referenced in Homer may have simply been too intellectually tempting to resist.
All of this has focused on the Greco-Roman understanding of the pyramids. Perhaps Cleopatra, who - uniquely among the Ptolemies - took the time to learn Egyptian, had a broader understanding. But in the absence of any definite evidence, we cannot be sure.
(1) Pliny, Natural History 36.76 (2) Appian, Civil Wars 2.90 (3) e.g. Histories 2.100 (4) 2.145 (5) 1.44.1 (6) 1.62.1 (7) 17.33 (8) 36.79