Mtskheta was the capital of the ancient kingdom of Kartli and served as Georgia's religious and political centre for centuries before Tbilisi took over that role in the 5th century. It remains the spiritual home of the Georgian Orthodox Church — the Catholicos-Patriarch is still enthroned here — and the entire historic core is a UNESCO World Heritage Site.
The two monuments you come for are the Svetitskhoveli Cathedral, which dominates the town square, and Jvari Monastery, perched on a cliff above the confluence of two rivers a short drive away. Both are extraordinary, and the views from Jvari back down over Mtskheta are among the best in the country. Adding Samtavro Monastery, just north of the cathedral, rounds out the visit — it holds the tombs of Georgia's first Christian monarchs.
The town itself is small and compact. Half a day is enough to see the main sights; a full day lets you explore at a more relaxed pace and have lunch. Mtskheta is just 25 km north of Tbilisi and an easy day trip by bus or taxi.