Some of Greece’s top sites are close enough to Athens for an easy day trip.
Here are a few:

Delphi, Greece

Delphi is a 2.5 – 3 hour drive northwest of Athens on the slopes of Mt.Parnassus, a really stunning spot. The ancient Greeks believed it to be the center of the world. According to legend, Apollo killed the Python that guarded the Omphalos, or navel of the earth, and thereafter, the site was dedicated to the god. The Delphic Oracle was a priestess known as the Pythia, who channeled the words of Apollo for seekers of wisdom from near and far. Delphi was also known for the Pythian Games, similar to the original Olympic Games.

The extensive remains are mostly from the 6^th-century BCE and are scattered on several terraced levels right down the side of the mountain. The small museum holds artifacts found at the site. The modern town of Delphi is right there, with lots of hotels, restaurants and shops. Staying a night instead of doing the roundtrip to Athens in one day is a good option. There are motor coach tours either way.

Lions Gate, Mycenae, Greece

Located about 60 miles southwest of Athens on the northeastern Peloponnese, in the region of Argolis, Mycenae was a major center of power in the eastern Mediterranean from about 1600-1100BCE. The Mycenaeans were culturally influential and the period is the source of a lot of Greek legend. Homer’s Iliad and Odyssey sprang from this time. In the Iliad, Agamemnon, the legendary king of Mycenae, led the Greek forces in the Trojan War. War sparked when Helen (of Troy) ran off with Paris, prince of Troy. Helen was the wife of Menelaus, King of Sparta and Agamemnon’s brother. It’s a good story, really. Whether any of the bones of the story are factual is debatable but there’s no question that it was inspired by some complex power struggles, think Game of Thrones.
(See my brief retelling of the Iliad here and here.)

Excavations at Mycenae represent different periods, ranging from 17^th-century BCE shaft tombs to the 14^th– century cyclopean walls (so called because the stones are so large the Cyclops must have built them) and the 13^th-century Lions Gate. A fair bit of walking over very uneven ground is required to see the site. Good, sturdy shoes are a must, and a big bottle of water.

Theater of Epidaurus, Greece

About an hour drive from Mycenae is Epidaurus, on the Saronic Gulf. In mythology, Epidaurus was the birthplace of Asclepius, son of Apollo and god of healing. The Asclepion sanctuary there was an active healing center from the 6^th-century BCE to the 4^th-century CE and then continued as a Christian healing center for another century. The area thrived on the popularity of the sanctuary and the spectacular theater is one indication of that prosperity. The theater seats 15,000 and the acoustics are so perfect that normal voices on the stage can be heard clearly from every seat. The theater is still used for performances today.

Napflion, Greece

The capital of Argolis is the sweet seaside city of Nafplio, widely considered one of the prettiest towns in Greece, which is really saying something. If you’re on a day trip from Athens, at least stop here for lunch and walk around the narrow alleys of the Medieval Old Town. If you’re on a longer tour of the Peloponnese, this is a good place to overnight.