The Mtskheta monasteries outside of Tbilisi, an easy daytrip from the city. And also a trip to the David Gareja Monastery, a UNESCO site on the border with Azerbaijan.
Svetitskhoveli Cathedral, called the Life-giving Pillar, is one of the most sacred places in Georgia. It was founded in 1010 and contains the graves of the ancient Georgian kings. In Mtskheta, Georgia.