Best time to visit

You can visit Tbilisi pretty much year around. Winters are pretty mild (~50 degrees F or ~10 degrees C) and prices are pretty cheap during that time. May offers warm weather, flowers blooming and New Wine Festival is held the first week of the month. July and August are the prime and hot months (can get up to ~80 degrees F or ~30 degrees C).

However, if you are planning on visiting Kazbegi, which you definitely should, best time would be summer - between July and September. in my opinion, the best time to visit Georgia for 8 or 10 days itineraries is September, when it's not too hot in Tbilisi, Kazbegi are still accessible and warm enough and crowds and prices go down.