This 7th century holy place is one of the holiest sights in a country full of holiest sights and is also the source of the mountain's name - Mtatsminda, which means "Holy Mountain". This was considered the Mt. Athos of Georgia, though it has suffered from invasion after invasion. The current church dates to the 19th century.
Though it's true that the church itself is only from the 19th century, the sight is an ancient place of prayer and one can still feel it, especially with the view of all of Tbilisi and far into the Caucasus - on a clear day, you can see Kazbegi. Also, all the famous Georgian writers and authors are buried here, called the "Georgian pantheon."
Wear some hiking shoes, the walk up to the church is grueling.