Svetitskhoveli (The Life Giving Pillar) Cathedral
Svetitskhoveli is one of the most sacred places in Georgia and, along with Jvari Monastery, the clear highlight of a trip to Mtskheta. It was founded in 1010, built on the site of Georgia's first church, and contains the graves of the ancient Georgian kings, including Sidonia, who was said to have been buried holding Christ's robe. There are many (unaggressive) beggars at the entrance gate.
The 6th century monastery of Jvari is situated on a cliff above Mtskheta. It is the culmination of a number of artistic and architectural aspiration in early Christian Georgian architecture. The view from above is great.
Be sure you travel there when there's clear weather and before dusk.
Samtavro (Place of the Ruler)
Samtavro is located to the north up the main road, within easy walking distance from the Svetitskhoveli complex. According to legend, St. Nino actually lived on this site and prayed within the smaller of its two extant churches. This small church dates from the 4th century. The larger church on this site was built in the 11th century and contains the graves of Mirian, the Georgian king who adopted Christianity, and his wife.
Bebris Tsikhe (The Elder's Fortress)
Located further up the main road from Samtavro, the ruins of Bebris Tsikhe are fun, if a bit dangerous, to climb on for views overlooking Mtskheta and the valley formed around the Mtkvari and Aragvi rivers.