Greek legend says that the king of Athens jumped from a cliff into the water below, forever tying his name–Aegeus–to the Aegean Sea into which he fell. Cape Sounion is where he is said to have jumped.
Cape Sounion sits at the southernmost point of mainland Greece outside Athens. In addition to the promontory's legendary importance, there are also ancient ruins you can visit nearby. There is a Temple of Poseidon dating from the 5th century B.C.E., into which the poet Lord Byron reportedly carved his name in 1810. Because of its geography, Cape Sounion is also a popular spot from which to watch the sun set into the sea.
Archaeological work continues today at Cape Sounion, but the area is more commonly known as a retreat from Athens. Many wealthy Athens residents keep second homes here, and many of the day-trippers to Cape Sounion are Athenians–not just foreign tourists.
Cape Sounion is roughly 76 miles from Athens by bus, and there are many day tours to the area from Athens. Bus tours typically start arriving at midday, so if you can arrange to be there earlier in the morning you'll have a better chance of seeing the temple ruins without the crowds.