The Panathenaic Stadium or ‘Kallimarmarois spans was constructed in the 4th century BC and is the place where the first Modern Olympic Games took place in 1896.  It is a real treat to run inside the stadium. Run around the horseshoe shaped dirt path inside the stadium or up and down the marble stairs. A nice time to run is in the evening, when there is a clear lit view of the Acropolis.  Note: Admission ticket required

The stadium is also the finishing line of the Athens Marathon, the Authentic which takes place every November.

DC Rainmaker has a nice write-up on the stadium and the running experience.

Add-Ons: National Gardens, right across the street. Also the path to the Athens Gate, taking you by the Temple of Olymian Zeus. Or, make it a grand tour, and include the Acropolis!

Write up of stadium National Gardens Run Acropolis Run