We'll start up there, at the historic, cultural, and literal high point of any trip to Athens — the Acropolis.

Like other hilltop sights in the ancient Greek world, Athens' Acropolis (or "high city") was both a place of worship and of refuge when under attack. Crowned by the mighty Parthenon temple, the Acropolis rises above modern Athens, a lasting testament to Greece's glorious Golden Age in the fifth century BC.

Grand processions followed the Panathenaic Way, which was a ceremonial path connecting the town below and the Acropolis. They’d pass through this imposing entryway and up to the religious heart of the city and the Parthenon.

The Parthenon was perhaps the finest temple in the ancient world. Valiantly battling the acidic air of our modern world, it still stands with the help of on-going restoration work.

It was constructed in the fifth century BC and dedicated to the virgin goddess Athena. Seeing it today is awe-inspiring but imagine how striking it must have looked when it was completed nearly 2,500 years ago — in all its carved and brilliantly painted splendor.

The adjacent Erechtheion is famous for its Porch of the Caryatids, six beautiful maidens functioning as columns. Dedicated to Athena and Poseidon, this was one of the most important religious buildings on the Acropolis. This, rather than the Parthenon, was the culmination of the Panatheniac Procession.

At the foot of the Acropolis, the Ancient Agora or marketplace sprawls out from its surviving temple. This is where, for 3,000 years, Athenians gathered.

While the Acropolis was the center of ritual and ceremony, the agora was the beating heart of ancient Athens. For some 800 years, starting in the sixth century BC, this was the hub of commercial, political, and social life.

Visitors wander the remains of what was the city's principal shopping mall and administrative center. Exploring the agora, it's fascinating to ponder the world of Plato and Aristotle and the age which laid the foundations for Western thinking about economics, democracy, logic, and more.

The Stoa of Attalos, from the second century BC, was rebuilt in modern times to house the Agora's museum. With so little of the Agora still standing, this reconstruction makes it easier to imagine the sight in its original glory. Crowds would gather in shady porticos like this to shop, socialize, or listen to the great philosophers of the age.

In fact, Socrates spent much of his life right here preaching the virtues of "nothing in excess," and urging those around him to "know thyself."

The Temple of Hephaestus, one of the best-preserved and most typical of all Greek temples, dates from about 400 BC. Like the Parthenon it's constructed in the simple Doric style. It housed big bronze statues of Hephaestus, the blacksmith god, and Athena, patroness of the city.

Greek architecture evolved in stages. The capitals, or tops of the columns, were both functional and decorative. While just the tip of the architectural iceberg, these are handy indicators helping us identify the three main architectural "orders" (or styles).

The earliest style, Doric, has flat, practical plates as capitals. In the next order, Ionic, the capitals are decorated with understated scrolls. The final order, Corinthian — popular later on with the Romans — features leafy capitals… boldly decorative with no apologies necessary.

How to remember all these? As the orders evolve, they gain syllables: Doric, Ionic, Corinthian.

But for most travelers, the agora is more than an architectural review. Strolling in the footsteps of Socrates is your best opportunity to commune with the epic Greek past.

Like so many great civilizations, ancient Greece peeked and then faded. Two hundred years ago, Athens was just a small town surrounded by big ruins, sitting on lots of history. That 19th-century Athens is today's Plaka.

The Plaka district provides tourists with a more intimate Athens: no chaotic traffic, lots of colorful restaurants, and the best souvenir shopping in all of Greece.