Daphni Monastery dates back from 11th century. Surprisingly, it fell in disrepair at the time of Greek War for Independence in 1830s. Now the monastery is a UNESCO site.
Monastery conists of a main church, which features amazing frescoes, a tiny museum, and, what appears to be, excavation sites.
To see everything will probably take about 20 minutes. (Those who love to admire beautiful frescoes and take photos will spend longer time) Thus, it is up to you whether you want to head there.
It will take about 30 minutes to get there from the center. Take M3 line to Agia Marina (going in the direction opposite to airport). Once exiting subway station, walk away from the main street into the neighborhood to the intersection of Agias Marinas & Katsarou Streets. The bus stop is nondescript and one can walk past it without realizing it. Take either bus 866 or 876. (Don't forget to wave the driver, the first bus randomly drove by even though there was clearly a person waiting for the bus). Google maps will direct you to exit the bus at Byzantiou stop, but get off at an earlier stop, which is appropriately called Daphni Monastery. Also, press the stop button, since the driver might just drive past the stop. Cross the street and walk roughly 200 meters.
In the off tourist season, the Monastery is opened from 8.30 to 3.30 Wednesday to Sunday.
If you have a limited time in Athens (less than 3 days), then this attraction is generally skip-able.