Actually, we arrived late, and just wanted something quick and easy so we could start exploring the city. When we arrived by metro at the Syntagma Station, we were surprised to see a huge, glass covered wall of dirt. The cut-away contained artifacts, drainage pipes, remains of a grave, and other antiquities. 
This was all found during the digging for the subway station -- and we found many other places like it all throughout Athens. Seems like wherever they dig, they find stuff. Another example was found while we were walking down a busy street. We came upon a large open hole that had been dug during construction of an air vent for the subway. They had found the remains on an ancient Roman Bathhouse. It was fascinating! 
The next morning we took an all day tour to Delphi, a beautiful archaeological site about 3 hours north of Athens. The ancient Greeks believed Delphi (correctly pronounced Delfee) was the "navel of the earth" and the center of the universe. According to Greek myth, Zeus released two eagles from opposite ends of the earth and they met in the sky above Delphi. Impaling one another with their beaks, they fell to the ground on the very center of the world. If you saw the movie "300", or know your history, you'll remember that this is where the Oracle lived, and presented her prophecies at the Temple of Apollo. It is thought that Delphi was first inhabited about 15th century BC.
According to Greek history, the oracle at Delphi was known as the Pythia. Apollo spoke through his oracle, who had to be an older woman of blameless life chosen from among the peasants of the area. She sat on a tripod seat over an opening in the earth. According to legend, the serpent Python was the ancient guardian of Delphi's Castalian Spring before he was killed by Apollo. When Apollo slew Python, its body fell into this opening in the earth, and fumes arose from its decomposing body. Intoxicated by the vapors, the oracle would fall into trance, allowing Apollo to possess her spirit. In this state she prophesied. She spoke in riddles, which were interpreted by the priests of the temple, and people consulted her on everything from important matters of public policy to personal affairs.
It was a beautiful drive, and an interesting day. Here are some pictures:
This is Mike and me standing by the remains of the Temple of Apollo. It dates back to 4th century BC. The rectangular pit to our right is where the Oracle Pythia was kept.The next day, we spend the morning walking all over Athens. Most of the major sites are within 10-15 minutes walk of each other, so it was quite an efficient site-seeing tour. We climbed up to the huge hill upon which the Acropolis sits -- it was a long, steep walk! This overview gives you an idea of how high it sits above the city.
Here we are in front of the ruins of the Parthenon:
Below you'll see a photo of the Erechtheion -- with it's much photographed "Porch of the Caryatids". The six ladies holding up the roof of the porch are replicas -- the originals were removed because of damage from pollution. One of the originals was taken by the pilfering Lord Elgin -- and the remaining five are in the Acropolis Museum. 
Of course there are many other ruins up there, but those were my favorites. We also visited The Temple of Olympian Zeus (seen below, and then another picture of a fallen column). This temple took over 700 years to complete, and only 15 of it's original 104 columns still stand.
This is Hadrian's Arch (with the Acropolis far in the background):
and the Roman Agora (marketplace):
We also toured the Greek Agora -- and the nearby Temple of Hesphaestus, the only Greek temple with an intact roof. Part of the peak is missing, but the columns are completely covered.
We also climbed up the rocky Areopagus, or"Mars Hill", where the Apostle Paul preached to the Athenians. It is spoken of in Acts Chapter 17: A group of Epicurean and Stoic philosophers began to dispute with him. Some of them asked, "What is this babbler trying to say?" Others remarked, "He seems to be advocating foreign gods." They said this because Paul was preaching the good news about Jesus and the resurrection.Then they took him and brought him to a meeting at the Areopagus, where they said to him, "May we know what this new teaching is that you are presenting? You are bringing some strange ideas to our ears, and we want to know what they mean. (All the Athenians and the foreigners who lived there spent their time doing nothing but talking about and listening to the latest ideas.) Paul then stood up in the meeting at the Areopagus and said: "Men of Athens! I see that in every way you are very religious. For as I walked around and looked carefully at your objects of worship, I even found an altar with this inscription: TO AN UNKNOWN GOD. Now what you worship as something unknown I am going to proclaim to you." ...When they heard about the resurrection of the dead, some of them sneered, but others said, "We want to hear you again on this subject." At that, Paul left the Council. " Here is a picture of Mars Hill:
That afternoon, we took an hour long bus ride out to Cape Sounion. It is a beautiful place, surrounded on 3 sides by the azure blue Aegean Sea. On top of the cape, is the Temple of Poseidon. The columns that are still standing have been there for over 2500 years. 
That evening, We had a delicious dinner at an outdoor restaurant in the Plaka -- the old historic part of town. After we ate, we walked the city at night and enjoyed some breathtaking views of the Acropolis. 
Sunday morning we walked up to the Parliament House and watched (before getting pushed out of the way by crowds) the changing of the Evzone guards at the Tomb of the Unknown Soldier. These colorful characters are clad in the traditional pleated kilt, white britches and pom-pom shoes made famous by the Klephts, the mountain fighters who battled so ferociously in the War of Independence. The soldiers' skirts have 400 pleats, one for each miserable year of Turkish/Ottoman occupation (and don't you forget it). 
Unfortunately we had to leave on Sunday afternoon. Our trip was too short, but we felt like we got a good taste of Ancient Greece. It really gives you an understanding of just how young our own country truly is. Hope you enjoy our trip along with us!