Mtskheta-Mtianeti begins right outside Tbilisi and climbs. At the bottom is the ancient capital Mtskheta; higher up runs the Georgian Military Road with Ananuri fortress and Gudauri. Everything is strung along one road, which is why it is usually taken as a single route.
All year, but differently: winter for snow at Gudauri, summer for green slopes and the pass. In winter the stretch above Gudauri sometimes closes for avalanche risk, decided in the morning.
Tell us when you are going and who with, and we will come back with a route and a price. A real person who knows these roads does the working out, not a calculator. No prepayment.