Focus on Tbilisi, the fascinating capital, with an outing to Mtskheta and a day trip to the spectacular Davit Gareja cave monastery.
Starting with Tbilisi, you have time to visit the mountains and another region too. Opt for two or three nights in either Kazbegi or Svaneti (to fit Svaneti into this schedule you’ll have to fly at least one-way). Have a couple of nights in the eastern wine-growing region of Kakheti (including a visit to Davit Gareja), or head to the cave city Vardzia via Borjomi and maybe have a day walking in Borjomi-Kharagauli National Park.
You can fit in all the destinations of the one-week itinerary, plus Gori, Kutaisi and the Black Sea resort of Batumi.