Georgia is not one country — it is four, and most tourists see two

Most flights from India arrive in the small hours. Day one begins with sleep. Once you are up, the old town is twenty minutes from the hotel: Shardeni Street for a late lunch of khachapuri and a jug of house wine, then the glass Bridge of Peace across the Mtkvari into Rike Park. The park has a small amphitheatre, good river views, and the cable-car station you will use tomorrow. Georgian wine costs less than the soft drinks on the same menu, so order accordingly.

The cable car from Rike Park lifts you up to Narikala fortress and the Kartlis Deda statue — a woman holding a sword in one hand and a wine bowl in the other, which tells you most of what you need to know about Georgia. Walk down through Abanotubani, the quarter of domed brick bathhouses built over sulphur springs the city was literally founded on. A private room in the baths, with a scrub, costs around ₹800 a person and takes an hour. Book on arrival rather than online; the walk-in rate is the same.

Evening: the 1905 funicular up Mtatsminda hill for dinner above the city. The funicular station is a ten-minute walk from Rustaveli metro. Sit on the terrace, order one of the Georgian sparkling wines they actually export to France, and watch Tbilisi go dark. Skip the amusement park at the top.

East ninety minutes into Kakheti, where almost three-quarters of Georgia's wine grapes grow. The method — skins, stalks and juice sealed together in a buried clay qvevri and left to ferment without intervention — is on UNESCO's intangible heritage list, and the amber wines it produces taste like nothing bottled in glass. You visit a family marani for a tasting and a supra lunch: khachapuri, khinkali dumplings, grilled mtsvadi, walnut dishes, and toasts that go on longer than the food. Count on two hours at the table.

After lunch, Sighnaghi, the hilltop walled town. The twenty-eight towers of its circuit wall are walkable in parts and give a view across the Alazani valley to the Caucasus. Then Bodbe monastery, where St Nino — the woman who converted Georgia to Christianity in the fourth century — is buried. Back in Tbilisi by eight. Skip the industrial-scale tasting halls on the highway; they are built for buses, not for you.

North on the Georgian Military Highway. First stop Mtskheta, the old capital twenty minutes out, where two rivers meet and Georgia adopted Christianity in 337 AD. Jvari monastery sits on the bluff above with the confluence in full view; Svetitskhoveli cathedral is in the town below, its interior covered in frescoes that survived Persian raids and Soviet atheism both. Allow an hour at each.

Then Ananuri fortress on the Zhinvali reservoir — a short stop, worth it for the two churches inside the walls and the colour of the water. The Friendship Monument on the Jvari Pass announces the climb is over. From Stepantsminda, a 4x4 takes the rough track to Gergeti Trinity church at 2,170 metres. Mount Kazbek at 5,047 metres is directly behind it; the cloud decides whether you see it. Either way, the drive up is the experience, not the view. Overnight in Gudauri, on the pass, closer to the mountain than to the city.

Down off the Gudauri pass and west along the Kura valley to Uplistsikhe — a town carved directly into a sandstone cliff in the first millennium BC. Streets, a theatre, a pagan sanctuary and a winepress are all still legible in the rock. Bring water and real shoes; the site is exposed and the steps are original. The cave city takes about ninety minutes to do properly.

Continue west to Kutaisi, Georgia's second city. In the afternoon, the Prometheus cave: 1.4 kilometres of lit stalactite galleries, with a short underground boat ride through a flooded chamber at the end. Check into the hotel and eat at one of the riverside restaurants on the Rioni — Kutaisi is cheaper than Tbilisi and the kitchens are the same.

A last morning at Martvili canyon, forty minutes north of Kutaisi. An inflatable boat takes you between limestone walls once belonging to the Dadiani princes — the canyon is not long but it is cold, green and unlike anything else in the Caucasus. Back into Kutaisi for a quick walk around Bagrati cathedral, a UNESCO site being carefully rebuilt after a seventeenth-century explosion. Kutaisi International Airport is twenty minutes from the city centre. Check your airline's hand-baggage rules before you pack the wine.