Athens was the site of the first modern Olympic games in 1896, but the stadium where the events took place - the Panathenaic Stadium - predated those games by many hundreds of years.
The Panathenaic Stadium (also called Panathinaiko Stadio) we see today was built on the remains of a 4th century B.C.E. stadium, which was a refurbished version of a 6th century B.C.E. stadium. It retains its original name, built for the Panathenaic Games in about 566 B.C.E., although the original seating was wooden. In 329 B.C.E. it was redone in marble.
In 1869, the entire site was excavated and renovated, and in 1896 it was the setting for the first modern Olympic Games, when roughly 80,000 people packed into the white marble stands. Today, the stadium holds about 45,000. When Athens hosted the 2004 Olympics, the Panathenaic Stadium was the location for the marathon finish line.
The Panathenaic Stadium is located in central Athens, just southeast of the National Gardens. Admission is €3 for adults and €1.50 for students and seniors. Children under age six get in for free. The entry fee includes access to the site, an audio guide, and the right to run on the track. In fact, you can join Athenians who do their morning jog around the historic track from 7:30-9am. The stadium is open from 8am-7pm during March-October, and from 8am-5pm during November-February.