ALTHOUGH getting to Georgia from Scotland is by no means a short hop, arrival at Tbilisi International airport feels like it should be the culmination of a much longer journey. The first thing that hits you (if you go, as I did, in the middle of summer) is a distinctly exotic brick wall of heat, and then there's the inevitable double-take as you glimpse Georgia's deliciously alien writing for the first time. The language has its own 33-letter alphabet, the elegant, flicking letters of which look like they're formed from ornamental Persian swords.

This is all in a country just across the Black Sea from a couple of EU member states, a geographical position that has conferred on Georgia a tumultuous history that hasn't given way to a particularly stable present. The tragic week-long war with Russia in 2008 left a new set of psychological scars on the country and, in Abkhazia and South Ossetia, entrenched two separatist-controlled enclaves in the north.

The starting point of a strange but illuminating road trip through the country was a long, blissful sleep at the Rooms Hotel in Georgia's capital, Tbilisi. Housed in a former publishing plant in the hip middle-class Vera neighbourhood, Rooms is one of the most impressive design hotels I've seen, with an amazing attention to detail that runs all the way from stunning retro furnishings and lighting to specific aromas being assigned to waft around specific areas of the building. You'll pay Western prices for Rooms' level of luxury although you can bag a bed in a Tbilisi hostel for under a fiver a night. The eye-popping low cost of everyday goods – a box of cigarettes costs just 35p – is another aspect that makes Georgia feel further from home than it it is.

In the morning we set out for the historical monuments of Mtskheta, which together make up one of Georgia's three UNESCO World Heritage Sites. Perched on a rocky mountaintop a few miles north of the capital, Jvari Monastery dates from the late 6th century. A stern doorman stopped us from entering for unspecified wardrobe offences, but its astonishing setting was what interested us. We lingered for an hour or more to drink in the view over the town of Mtskheta and the confluence of the Mtkvari and Aragvi rivers. Mtskheta itself is one of the world's oldest continuously inhabited settlements, and was the capital of the Georgian kingdom of Iberia from the third to the fifth centuries. As such, it's hugely important to the nation, as well as being the obvious base camp for any visitor looking to binge on Georgian and/or Orthodox Christian history. With the help of free shawls at the door we made a more successful visit to the Living Pillar Cathedral in the town's historical Svetitskhoveli complex, before heading to a restaurant for the first of many absurdly generous lunches.

Georgian food is delicious and filling but it can get a bit samey if you stick to it too rigidly. The ubiquitous duo of vegetables stuffed with hummus-like substances (tolma) and flat slabs of bread with a gulch of melted cheese in the middle (Khachapuri) is great in moderation, but that’s not a concept that looms large in Georgian cookery. International alternatives abound though, particularity in Tbilisi. Churchkhela, a sweet, sausage-shaped stick made of dried and compacted grape must, nuts and flour, is an interesting oddity and packs enough sugar to perk you up in the middle of hot day of sightseeing but you're unlikely to want to smuggle bagfuls of them home with you.

A long wander around the huge flea market that sprawls over Tbilisi old town's Dry Bridge area left several lasting impressions, primary among them the realisation that paintings of Joseph Stalin are still very big business here. Uncle Joe was a Georgian, of course, and attitudes to him in the country are complex, but can be very loosely parsed along generational lines. Generally, the old like him, the young do not. Under the trees at the market, though, sun-dappled renderings of that giant-caterpillar moustache were everywhere, along with piles of Soviet memorabilia, endless household trinkets, and Russian versions of old pop records by Toma Jonesa and the like.

As we started to wind our way west, Tbilisi's urban sprawl was quickly replaced by some pretty down-at-heel little towns and stretches of countryside where subsistence farming seemed to be the dominant economic activity. For every stretch of driving like this, however, there was another that took us through a stunning valley or mountainous area, though these also tended to be the backdrop for some pretty hair-raising driving in a country renowned for it.

Our next stop was Tskaltubo, three hours west of the capital, and home of a place called Prometheus Cave, which sounds like a hot new rock band but is actually one of the best places in Europe to see stalagmites and stalactites. The kilometre-plus walk through the caves, with the thousands upon thousands of Pinocchio's-nose rock protrusions lit up in shifting colours as we passed, was an otherworldly, peaceful delight that doubled as glorious relief from the baking sun. A recurring theme in Georgia's tourism efforts is the pushing of various areas' health-giving benefits, and our hotel for the night was the ultimate expression of that. The Tskaltubo Spa Resort is a grand series of dazzlingly white, colonnaded buildings and Instagram-ready fountains in an area of nationally renowned healing Radon waters. The resort was updated and redeveloped in the late 1990s and early 2000s, but in its previous incarnation this was where Stalin – that guy again – came to take the weight off during his reign.

The next morning we pushed on towards the Black Sea coast in the country's south-west. I've seen several places in the world trade heavily on links with the Clintons (think Reykjavik's most famous restaurant: a Bill-endorsed hot dog stand), and Batumi, on the Black Sea by the Turkish border, is another for the list. Hillary visited in 2012 and described the place as “a kind of mini Las Vegas on the Black Sea”. As we were ushered into the garish luxury of the Leogrand Hotel & Casino, it became clear that the city has no problem with that image. Its extraordinary waterside skyline, which hoves improbably into view many miles away as you approach on the coast road, also speaks of grand ambitions. Its two most arresting structures might resemble the syringe of the future and a giant rocket but they're fitting symbols of a place on the up, and the hordes of wealthy tourists pouring in from the likes of Iran and Israel are likely to keep it that way.

More prepossessing than the city of Batumi, however, were a couple of stops in the outrageously beautiful countryside that surrounds it. First was the Batumi Botanical Gardens a few miles north. A vast garden that ascends gradually to a coastal clifftop, the place houses thousands of different kinds of plants and trees and, in the deep blues and greens of the view up the coast from the top of the gardens, a sight of genuinely world-class beauty. Adjarian Wine House, in the Adjara Mountains, was another of Clinton's stops in the region, with a combination of delicious al fresco dining and drinking and butter-advert scenery.

Back in Batumi, I stumbled (literally) into a fairly reasonable analogue for where Georgia is as a tourist destination right now. Seconds after departing the swishy glamour of the Leopold Hotel to take a walk along the much-vaunted Batumi Boardwalk, I found myself up to the ankle in muddy pothole water on a stretch of pavement that they were probably going to pave soon, but hadn't quite got around to yet. Like the streets just behind the polished boardwalk in Batumi, Georgia is still very much a work-in-progress. If you plan well and are willing to forgive the odd rough edge, however, then a land of great hospitality, dazzling natural beauty and endless historical interest awaits, all topped off with enough exotic cachet to satisfy the most adventurous of travellers.

Kit Macdonald flew to Tbilisi with Ukrainian Airlines from Gatwick Airport. Return flights in August start from around £332, with return flights via British Airways from Glasgow International to Gatwick at the same time starting at around £95.

He was a guest at Rooms Hotel Tbilisi, where rooms start at around £146, Tskaltubo Spa Resort, where rooms start at around £65, and Leogrand Hotel & Casino Batumi, where rooms start at around £108. All of these are based on a double room in early August.