The monastery belongs to the UNESCO World Heritage Site and has been renovated from 2005 - 2007.
The way up to the mountain is 7 km long and is like the best paved road I have seen in Georgia - you can choose to take a Taxi from Mtskheta.
The cache is a small box and it´s NOT hidden at the monastery itself. There is a fence just north of the monastery. You can enjoy the view to the monastery and to the city downhill in almost silence instead of being in the mass of tourists.