Four days in Tbilisi: a city that bathes in the morning and feasts until midnight

Start in the tangle of lanes that climbs from the river towards Freedom Square. This is the part of Tbilisi that survived, more or less: crooked houses built around courtyards, carved wooden balconies hanging over the pavement, churches wedged between apartment blocks, and the occasional abandoned tram parked where somebody left it. Nothing here needs a ticket. Wander, and let the streets do the work.

Then walk down to Abanotubani and the domes. The bathhouses are built into the slope so that only their brick cupolas show above ground, with the water arriving hot from the spring beneath. There is a public bath where entry costs a couple of lari and a row of private rooms you rent by the hour for a few tens. Take the private room if there are two of you, take the public one if you want the full experience, and take a towel and something on your feet either way. Add the scrub and soap wash, which is administered rather than offered and is the best twenty minutes of the trip.

Come out pink and useless, and eat nearby. Khinkali are the dumplings, ordered by the piece, held by the twisted top knot, bitten and drunk before they are eaten, and the top knot is left on the plate.

Cross to the left bank first thing for Metekhi, the small church on the cliff directly above the river. There has been a church and a royal residence on this rock since the fifth century; the current building is late thirteenth century, rebuilt after the usual catastrophes, and the equestrian statue outside is Vakhtang Gorgasali, the man with the pheasant. The terrace gives you the best single view of the old town, with the baths and the fortress lined up across the water.

From Rike Park below, the cable car crosses the river and lifts you to Narikala in about two minutes for a couple of lari. The fortress has held this ridge since the fourth century, though most of what stands is far later and much of it is frankly a ruin, which is part of the appeal: there are no handrails, no queue and no ticket, just walls you can climb on with the whole gorge underneath.

Then walk the ridge west to Mother Georgia, twenty metres of aluminium raised in 1958 for the city's fifteen hundredth birthday. She holds a bowl of wine in one hand for guests and a sword in the other for everybody else, which is as good a summary of the national character as anyone has managed. Walk back down through Sololaki rather than taking the cable car, and you arrive in the old town in time for dinner.

Mtskheta was the capital of Iberia for most of a thousand years, and it is where Georgia became Christian in the fourth century. It sits north of the city where the Aragvi meets the Mtkvari, and a marshrutka from Didube station gets you there in about half an hour for a couple of lari. A taxi for the day costs about as much as lunch for two in Berlin.

Do Jvari first, because it is on the hill opposite and the view is the reason to go early. The church was built around the year 600 over the spot where St Nino, the woman who converted the country, is supposed to have raised a wooden cross, and it is the model that Georgian church architecture copied for the next five centuries: a compact cross plan, bare stone, almost no decoration and perfect proportions. From the terrace the two rivers meet below you, one green and one brown, and the town sits in the fork.

Then come down to Svetitskhoveli in the town itself, founded in 1010 on the site of Georgia's first church. Kings are buried under the floor, and the pillar in the middle is said to stand over the robe of Christ, brought back from Jerusalem by a Mtskheta Jew who was there at the crucifixion. Whatever you make of that, it is the second largest church in the country and the walls of the compound around it make it feel like a small fortified town.

Samtavro is ten minutes further on foot, quieter and still a working convent, with the graves of King Mirian and Queen Nana, the pair who made the country Christian.

Save the Museum of Georgia for the last morning, because it explains everything you have spent three days looking at. The archaeology floor holds gold from the Colchis kingdom that gave the Golden Fleece legend its raw material, worked here so early that it influenced Persian and Greek jewellery rather than the other way round. Downstairs are the hominin skulls from Dmanisi in the south of the country, around 1.8 million years old and the earliest humans found anywhere outside Africa. Upstairs is the Soviet occupation exhibit, which is short, angry and unmissable.

Then walk to the Dezerter Bazaar near the railway station and buy what you are taking home. Churchkhela, the strings of walnuts dipped repeatedly in grape must until they set, keep for months and cost almost nothing. So do the spice blends, the dried fruit leather and the sulguni cheese, though the cheese will not thank you for a long flight.