The Monastery of Daphni was a World Heritage site, probably the best place in the world to see Byzantine mosaics. Then in 1999 it was hit by an earthquake. The whole place came very close to complete collapse. They've been restoring it ever since.
You can visit the Monastery even though it is being repaired. In October 2012, the opening hours were Tuesday and Friday only, 9am to 2pm. You have to ring the bell on the gate and they will buzz you in. Although the church which holds the mosaics is completely encased in scaffolding, both inside and out, if you hang around for a bit, a guide will bring you in and let you see the mosaics - you'll have to peer at them through the scaffolding, but at least they let you climb up high into the church and you can get really close to the priceless pictures.
Daphni is only about 6 miles from the city centre, so the easiest way to get there is probably by taxi, but you can get the A16 bus. Ask the bus driver to tell you when you're there.
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