So, I’ve got two things I think I can talk about with some authority. The first is about the original post you mentioned and Egyptian citation of place through time. The second point I can make is about ancient and pre-Colombian Mesoamerica. Though I imagine there are experts here on both points better informed than I. Both of these points are not directly in my line of expertise, but I have worked with them in an ancillary fashion before.

First, our Egyptian example. The scale of Egyptian history is enormous; “civilization” has flourished in the Nile river valley for literally millennia. Early monumental architecture (think early steps towards what become famous later as the pyramids) appeared after the unification of upper and lower Egypt in the Early Dynastic period. These are of course only the more obvious and lasting signs of a shift to cereal cultivation and a switch to (at least partially) sedentary lifestyles. For simplicity sake, let’s just think of this period as “3000 BCE”. The Ptolemaic dynasty, which really is of the Classical time period rather than the Ancient, can be simplistically remembered as “300 BCE”. That means that for the residents of Egypt in the Ptolemaic dynasty, the Early Dynastic monuments were as ancient as are the crumbling Classical temples to the modern-day residents of Greece.

In a relatively geographically circumscribed area like the Nile valley, space is at a premium. This, in part, led to the reuse of tombs in later periods. At some locations, vibrant communities of the living (in this case a walled workers village) could be abandoned by the living, but used for multiple hundreds of years afterwards as mass cemeteries and religious locations – with new temples built atop old temples hundreds of years later (see work on Deir el-Medina, here and here. )I imagine this sort of reuse should be familiar to any modern person – we need only look to our re-use of sites in Jerusalem over the past few thousand years to understand this sort of re-use. These markers of use (cemeteries, temples, etc) are just that – markers of the presence of humans moving through space. The physical vestiges of history they themselves moved through –as they created their own – would have been experienced in much the same way that you or I would tour the crumbling Acropolis.

The second example I feel able to discuss is the Mesoamerican case I mentioned above. The urban center of Teotihuacan was founded in the period you mentioned (a timeframe like 500 BCE to 1 BCE.) and abandoned by the middle of the first millennium of the CE. The city sits roughly 25 miles north east of what would become Mexico City. When the Aztec empire rose to prominence, the leaders of that polity would make annual trips to Teotihuacan to “pay their respects” culturally and religiously, for lack of a better phrase. The current theory goes that as foreigners to the area, when the Aztecs needed to justify their rule, they made allusions to the Teotihuacanos of more than a millennium ago, incorporating their motifs and stylistic elements into their monumental architecture in Mexico City, and placing an Aztec monument (I believe it was a stelae, but I don’t have my papers in front of me…) in the ruins of Teotihuacan.

Actually I just found an electronic version of my old (5+ years) undergraduate honors thesis with a relevant section. Forgive the copy-pasta (“it” is Teotihuacan):

“It was already in ruins when the Aztecs began to use it to legitimize their rule at Tenochtitlan. The Aztecs, using the legacy of the (already ancient) city to claim cultural descent even though they were really nomadic peoples from far to the north, referenced Teotihuacan architecture (See Figure 1) and art. They placed their origin story at Teotihuacan, and during some periods, the Aztec ruler travelled from Tenochtitlan to Teotihuacan as often as every twenty days to perform rituals (Hamann 2002: 351).”

I continue later:

“But reuse of sites is another way in which politics can be inscribed into the landscape in the form of monuments. When the Aztecs used Teotihuacan and its material markers to legitimize their rule in the Basin of Mexico, they constructed their own monuments at the site, at least one of which may have been located in the plaza in front of the Pyramid of the Sun (Umberger 1987: 83). The commission of this monument was specifically designed to leave an indelible marker of Aztec presence in the landscape. The same sort of cooption of cultural identity takes place at Tenochtitlan, only in reverse. The Aztecs built Teothiuacano style temples near the site of, or on top of, the Templo Mayor. This referential architecture is still visible today in the form of the Red temple (See Figure 5)”

So, back to my answering your question. I know you asked about something that didn’t have “contemporary religious significance” and I know that it could be argued that both examples I gave you fall into that. But I hope you’ll see that there was also (in the second) massive politico- and historico-cultural overtones to the religious allusions, and heavy historical and cultural reasons for re-use at Deir el-Medina as well. Anthropologists (a group in which I self-identify) have the problem of often using the idea of religion or spirituality as a crutch as well – using it as a catch-all for unanswered questions or motives. Some of that may be creeping in here, though I hope not un-critically.

I think you’ll find if you delve into the site-history of any long standing monumental area, you will find historical examples of re-use that would qualify as touristy behavior. It is absolutely nothing new to modernity.

One place to look is Pagan Holiday: On the Trail of Ancient Roman Tourists (2003) by Tony Perrottet, describing the advent of intercontinental tourism within the Roman Empire given the relative safety of travel established for its citizens. That said, the accuracy of his research and his overall assessment have been challenged, and so it is worth remembering what you note, that "ancient people lacked resources to travel very far," and also that the world was still much more dangerous back then.

I'd say absolutely. The Seven Wonders of the World were decided in antiquity, pointed out for the benefit of ancient travelers.

One example might be Alexander the Great, who visited the tomb of the Persian King Cyrus and ordered it open to view his body. Centuries later, the Roman emperors would do the same to his tomb in Alexandria.