On the road from Tbilisi to Telavi you'll definitely pass the Ujarma Fortress, which was founded in the III century. However, it's not easy to notice it, so be attentive and look for the signs. In the V century, King Vakhtang Gorgasal made it his residence. In the X century the fortress was destroyed by the Arabs, and in the XII century the upper part was restored by King George III, who kept there his treasures.
At the time of our visit in 2012 there was a small renovation of the territory around the fortress. It's not fully preserved, however, it's located on a high hill with scenic views.
Getting there: The fortress is usually visited during a day trip to Kakheti. Unfortunately, I have no information about the buses that may go to the fortress. It is located on the road from Tbilisi to Telavi, maybe some minibuses go there.