Sioni Cathedral and the Gabriadze clock tower, lunch in the old town, the cable car to Narikala and the Botanical Garden waterfall.
Day 2
Baths & the river
A morning private room in the sulphur baths, Jumah Mosque for Dhuhr, Metekhi and the Bridge of Peace at sunset.
Day 3
Rustaveli & the hills
The Georgian National Museum, a walk along Rustaveli Avenue, then the funicular up Mtatsminda for the city lights.
Day 4
Mtskheta
Jvari Monastery on its hill and Svetitskhoveli Cathedral below, back by mid-afternoon.
Day 5
Kazbegi
A long day up the Georgian Military Road past Ananuri to Stepantsminda and Gergeti Trinity Church.
Day 6+
Go deeper
Sighnaghi and the Kakheti harvest, Turtle Lake and the open-air museum, or slow mornings at Fabrika.
Honest thought: the old town is hilly and cobbled, and the best sights sit on steep slopes. Use the cable car and funicular, keep each day to one area and save the mountains for a clear-weather forecast.