Updated: Jul 14, 2021
Not that it's a contest, but the ruins of ancient Rhamnous are not only a lot more ancient than those of Machu Picchu but also immeasurably more evocative, given the setting. While the overhyped mountaintop Incan citadel dates from the 15th-century AD, the largely intact ruins of Rhamnous, strategically perched above the Euboean Strait of the Mediterranean Sea about one hour north of Athens, stretch back to the sixth century B.C. Think about that for a minute.
And if you visit this mysterious place you will for sure be given to reflection, because there will be almost certainly no one else around. Despite its important role in Greek history, its fortified acropolis and its ancient fame as the site of the Sanctuary of Nemesis—that badass goddess of vengeance and divine retribution—today Rhamnous basks in its brilliant and silent obscurity. From just about anywhere, it's a schlep. There are no stores or cafes nearby, just olive trees (lots of them) so if you don't bring enough water you might faint from the heat. If you don't make it to the entrance by 2pm they won't let you in because the site closes at 3 and the walk from the entrance gate to the sanctuary and ruins beyond is long and rock-strewn, as if Nemesis is trying to tell you something (like Keep Out). I highly recommend it.
Here's some history for you, right from the source:
Throughout the site there are are guards (not guides) who are essentially monitoring your movements at what is perhaps the biggest least-known active archaeological site in Greece.
On the way back to Athens, you might want to stop in Marathónas (Marathon) -- yes, it's the original one, where the Athenians beat back the Persians in 490 B.C. But you'll need several hours to visit all the sites of Marathon properly.