As understatements go, saying Greece has had a fair few problems over the last few years ranks alongside calling the Himalayas a little hilly. What with political upheaval, economic disarray, mass demonstrations and teargas-strewn riots seemingly a daily occurrence, it’s hardly surprising that the country’s been having trouble attracting overseas visitors.

That is, of course, unless you count the seemingly endless waves of distressed Middle Eastern migrants arriving by the hourly boatload. Add in images of the Aegean islands being overrun with makeshift refugee camps and it soon becomes clear why Greece is largely omitted from most folk’s Top Ten Places To Go For a Stress-Free Relaxing Vacation.

Appearances, however, can be deceptive. Although to the outside observer Greece might seem to be on the verge of economic and social collapse, the reality is markedly different, as anyone who braves a trip to its shores will pretty soon come to realise.

Arriving in Athens, the country’s bustling capital, you would have to work extremely hard to see it as anything other than a typically prosperous European city. The roads hum with traffic, the public transport is sleek and efficient, the shops are busy and its restaurants and bars seem ever full.

Contrary to popular belief, there are no queues of angry customers outside the banks, all trying to withdraw their last euros while they still can.  Everyday Athenian life, in fact, seems resolutely normal.

There are still some signs, however, that all is not entirely well. Any city with a high percentage of its walls covered in angry-looking graffiti – largely consisting of the initials of various political parties – is not necessarily one at ease with itself.

But at the Plaza Syntagma, the huge central square that became the focus of frequently violent anti-austerity demonstrations, the protestors and the police appear to have given up and gone home. Now it once again caters solely to strolling couples and street vendors. And, of course, the thousands upon thousands of tourists who turn up for a bemused gawp at the evzones, the bizarrely-dressed soldiers who parade outside the parliament building.

It’s actually quite difficult to see what use the evzones would have been had any of the rioters been truly intent on doing damage to their duly-elected representatives. They are not really the most fearsome-looking of sentries. Their uniform (tasselled fez, short skirt, white stockings and pom-pommed clogs) and weird ceremonial march (goosestep, pirouette, balance on one leg for a bit) appear designed more to provoke hilarity than terror.

Strangely enough, the costume was not created by some Jean-Paul Gaultier-type couturier on one of his more eccentric days. Instead, it’s a respectful nod towards the uniform of the klephts, resistance fighters who battled the ruling Turkish forces for many centuries at a time when Greece was under the control of the Ottoman Empire.

Hopping about looking like badly-dressed clowns seems an unlikely military strategy for defeating an occupying army. But don’t tell the Greeks that. They’re rightly very proud of their history.

And so they should be, as they seem to have so much more of it than most other countries. Remnants of its glittering past are literally everywhere – and nowhere more so than in Athens, with the city flowing out from round the ancient rock of the Acropolis.

Squatting imperiously atop this edifice, like some doughty dowager duchess peering disapprovingly down on her unruly grandchildren, is the vast temple of the Parthenon. It’s a stiff climb to access its precinct, but the greater challenge is to take a photo of it without getting any scaffolding in the shot. The site is currently undergoing a massive restoration and repair programme – though, in fact, the truly astonishing thing about this ancient site is just how much of it has actually survived.

In the 25 centuries since it was constructed, it’s been ransacked, renovated, looted, shelled, set ablaze, turned into a mosque and used as an ammunition dump. It’s endured marauding pirates, invading Turks, English aristocrats intent on stripping its glories and even the pollution of the Athens traffic. Yet it remains – largely – intact.

Sadly, the same cannot be said of all of Athens’ antiquities. The colossal Temple of Olympian Zeus, once boasting more than 100 mighty columns, now has just 16. Another lies rather sadly in pieces, symbolically strewn across the site. On the bright side, it’s so far gone there’s no point sticking scaffolding up to save it.  This allows you to walk round it unimpeded, imagining the temple in all its former glory.

Some former glories, however, you don’t need to imagine. The ancient amphitheatre, the Odeon of Herodes Atticus, built into the Acropolis hill, for instance, has had its seating and stage magnificently restored and now hosts the Athens Festival each year.

Then there’s the Panathenaic Stadium, originally built in the sixth century BC as a site to honour the goddess Athena with displays of athletic prowess. In 1896, it was faithfully reconstructed in every detail in time for the first ever modern Olympics – marble seats, elongated running track and all. It was called back into service to host the climax of the marathon race when the Games came back to Athens in 2004. It is now open for visitors to wander around at a less frenetic pace.

Should the mood take you, you can even have a quick sprint around the track and pose on the medal podium, selfieing yourself as one of the sporting heroes of Ancient Greece. It’s probably best not to take this particular fantasy too far though – in those days they used to compete largely in the nude.

Another ancient site completely rebuilt as near to the original as possible is the impressive Stoa of Attalos in the Agora (ancient marketplace). It was reconstructed by the American School of Archaeology in the 1950s and now sits among the rest of the ruins housing a superb museum, home to many of the more memorable finds from the nearby digs.

Even if you’re not normally a huge fan of museums, this one is worth a visit and it won’t even take you all that long. Among its attractions are some truly fascinating finds – such as the original stone-carved tablet setting out ancient Athens’ democratic principles, a sort of marble Magna Carta or dacite Declaration of Independence.

While Athens is truly an impressive city, its dust and the heat do make it hard to endure for more than a few days at a time. Thankfully, a number other equally fascinating destinations are just a day-trip away. Most notably, several of the country’s more beautiful offshore attractions – the Saronic Islands – are accessible via a short ferry ride from the port of Piraeus.

Hydra is one island that comes particularly recommended. It’s a sort of environmentalist’s paradise where cars are totally banned. For many, though, neighbouring Aegina is actually far more interesting. Once a great naval power and very much a rival to Athens, it now thrives mainly on tourism, fishing and pistachio nuts (they claim to have the best in Greece and sell them by the barrowload).

Aegina also boasts the Temple of Aphaia, a sacred site older even than the Parthenon. It was once decorated with scenes depicting the Trojan War, which, to the builders of the temple, was pretty much recent history, having taken place just a few hundred years before. It seems incredible to be walking round a building constructed at a time when stories long morphed into myths were actually comparatively recent headlines.

Back on the mainland, the coast of Attica is also well worth exploring. The bars and beach clubs of Alimos, Glyfada and Vouliagmeni are where the country’s well-to-do hang out. They are very relaxing resorts, though only if you like your sunbeds arranged in regimented rows up and down the sands.

Vouliagmeni does, however, boast a more unusual and interesting attraction – a large lake, half seawater, half freshwater and heated by a thermal spring. Given its dramatic setting – deep, dark waters at the foot of a dizzyingly-high sheer cliff face – it’s small wonder it’s reputed to have healing qualities.

Inevitably, it has a spa attached to it, but the 13-euro (HK$107) entry fee is reasonable enough and the staff reassuringly unobtrusive. Whether the lake actually has healing powers is, of course, debatable. What it undeniably has, however, are thousands of little fish, all only too keen to nibble away at your dead skin should you stay still in the water for even a few seconds.

It’s an initially uncomfortable feeling, but you soon get used to the slightly tickly sensation of being exfoliated by these particular finny friends. Some like it so much they let whole schools of fish cover their body from neck to toe. That, however, is very much an acquired taste.

Once you’ve had enough of being pecked at by piscine predators, you should head down the highway to Cape Sounio on the southern tip of the Attican coast. It’s a long drive, but here, on a clifftop above the Aegean Sea, sits the famous Temple of Poseidon.

It’s an incomparably beautiful view, one that the poet Lord Byron was so taken with he implored the gods to let him die there. Most visitors aim to get there in time for sunset, when the stark white columns of the temple stand out against the crimson sky and the Aegean turns from a sparkling sapphire to a deep imperial purple. It’s a challenge for even the most hard-hearted not to come over all poetic at the very sight.

Greece, it has to be said, does do sunsets rather well. Back in Athens, there’s a particularly splendid one, best observed from the summit of Lykavittos Hill, looking west towards the Acropolis. As the night falls and the colours of the sunset fade, you get a bonus – the sight of the Parthenon lit up with bright white lights, a shining star above the city.

Greece can truly beguile you with its beauty. On our last night in Athens, my partner and I found a restaurant tucked away on a cobbled side street, on the hillside by the Acropolis. We sat at a table on a balcony, aromatic jasmine draped along the ironwork, the illuminated Parthenon in the background, laughter and music drifting up from below. The scene seemed so far removed from the riots and austerity so long associated with Greece, that it hardly seemed to belong to the same country or period of time.

Greece is a country you must visit and Athens is a city not to be missed. Despite the recent ructions that have rocked its economy, there is a timeless beauty to the place. When the financial hardships and uncertainties have long faded from our memories, Greece will once again resume its rightful place as one of the true cradles of civilisation. Some would say it already has.