I rapped on the door and it creaked open as an old man in robes stood in the doorway, eyeing us suspiciously. What did we want, he demanded pompously of the group of Ukrainian girls standing next to us. Their answer — in Ukrainian and unfathomable to me — seemed to just about do, and he grudgingly let us through the door. But not before sternly reminding me to wipe my un-muddy shoes. As I entered the dimly-lit room, I took a moment to remind myself why I was here… in this eccentric Masonic Restaurant (named after the religious order) in Lviv, Ukraine's second-largest city.

Now several days into a first tour of the country, I had learnt, if nothing else, to expect the improbable. Twenty years after achieving independence, this pocket borough of the former Soviet Union veers between communist traditions and a burgeoning free market in a rather haphazard way. Constant reminders of Soviet times punctuated our journey. There were the grim Soviet-style buildings, of course. On trains we encountered stern old ladies running each compartment with a zeal for rules and regulations that wouldn't be out of place in a boarding school.

At the same time there were many moments of innovation and quirkiness, such as the Masonic restaurant, whose décor featured mysterious Masonic icons and whose facilities included a resplendent throne-like toilet. The restaurant proudly proclaims to be the “most expensive in Galicia” with menu prices 10 times local rates, so a visit must be preceded by a hunt of local shops for a 90 per cent discount card. In fact, they won't let you eat here without it. (Just down the road is an equally quirky place where you can climb to the terrace to sit in a beaten-up old car with a propeller attached).

Soviet and other anger

The Soviet history doesn't sit easily. In the capital Kiev, as well as Lviv, anger against the former Soviet Union borders on praise for the country's other invaders, of whom there have been many ranging from the Poles, to the Austrians and the British. “The Nazis gave our children chocolates but the Soviets killed them,” one taxi driver in Lviv told us with conviction. We came across large billboards and even T-shirts equating the Nazi Swastika with the Hammer and Sickle. Several days later, in the Crimean seaside town of Yalta (where the 1945 conference on the reorganisation of Europe took place), it was Soviet times that were yearned for. Ukraine, or at least Crimea, should rejoin Russia to become strong again, our guide told us. In the port city of Sevastopol, home to Russia's Black Sea Fleet, buildings and cars bore the red, white and blue flag of Russia rather than Ukraine's own blue and yellow. In this part of the country, much of the population is ethnically Russian; Russian is the main language of schools and of the street. There's even a statue of Lenin in Yalta, a summer holiday spot for many Russians since Tsarist times.

Chant against corruption

Modern-day politics is charged: Yulia Tymoshenko, who came to power in the Orange Revolution of 2004, now languishes in prison on charges of corruption, while pro-Russian President Viktor Yanukovych has stirred up controversy by agreeing to let Russia's Black Sea Fleet remain in Sevastopol beyond its existing lease of 2017. During our visit to Kyiv, the main street was filled with pro-Tymoshenko protesters chanting “Yulia! Yulia!”; they were also singing with gusto and waving tall flagpoles in a carefully choreographed dance.

One matter pretty much everyone we met seemed to agree on, however, was corruption, which they said was everywhere and not on the decline. A taxi driver spat out of the window after we drove past some policemen. Ukraine is a lowly 134 out of 178 on the Transparency International's Corruption Perception Index.

Tourism windfall from football

Enthusiasm for the Euro 2012 football championships, half of which will take place in Ukrainian cities, seemed to be another unifying force. Alongside new roads and infrastructure, people are hopeful it will finally give Ukraine the international attention it deserves as a holiday destination. Apart from Poles in the West and Russians in the South, we encountered surprisingly few foreign tourists: Ukraine still doesn't figure prominently on the tourist map. And there is plenty to see.

Kiev is dotted with beautiful churches, and the spectacular Lavra — a fairytale collection of monasteries and gold-domed churches on the city's outskirts. There you can walk through a maze of catacombs containing the mummified remains of monks, guided only by the light of your candle. Despite the large number of worshippers who visit, it doesn't feel hectic. Everyone keeps a respectful distance and silence down there; all women don headscarves. It is Ukraine's holiest site.

Awe-inspiring sites

Lviv too is littered with numerous baroque and Renaissance churches (it is a UNESCO World Heritage Site) too stunning to let site-fatigue set in. While the city itself is beautifully preserved, some of its palaces have a less happy fate. It was almost painful to look at Pidhirtsi Castle, a short drive from the city, falling apart with no effort to salvage it.

My most breathtaking moment was arriving in the village of Kamyanet-Podilsky in the heart of the country. You'd be forgiven for thinking you'd stepped into a mini-Switzerland, in the honey-coloured old town skirted by a gorge and guarded by a fortress. The fortress — first built in the 10th century and renovated in the 16th — is well maintained and, again, surprisingly empty; you can clamber over its ramparts with the freedom of a child.

Memories of another day

There were constant reminders of Ukraine's troubled past. Cemeteries and monuments to those killed in World War II and during Soviet times were everywhere, whether in cities or along country roads. The imaginatively done (though sadly lacking in English signs) Chernobyl Museum is a reminder of its most recent tragedy, with images of all those who perished in the world's worst nuclear disaster. There are tours of the site itself, though with an exclusion zone still in place it was a risk I chose not to take.

Down south in Crimea, we visited the site of the Battle of Balaklava, where the Light Brigade made famous by Alfred Tennyson's poem rode to their deaths. It is now vineyards.

In Odessa we walked down the steps that formed the setting for one of cinema's most famous scenes: a pram rolling down the steps as a frenzied crowd flees a massacre, in Sergei Eisenstein's Battleship Potemkin , about a mutiny against the brutal Tsarist regime. Balaklava could be just another picturesque village on a bay, but for the secret Soviet nuclear submarine base adjoining it, which is now a museum. It was easy to see why it is a country known for its dark, tragedy-tinged humour. Mikhail Bulgakov, author of the farcical masterpiece Master and the Margarita , was born in Ukraine (there is even a rather surreal museum to him in Kiev), as was its current literary star and author of the hilarious yet poignant Death and the Penguin , Andrey Kurkov.

An explorer's delight

Despite the language barrier — very little English is spoken here — there were many moments where I felt at home in Ukraine. But attitudes to women left me cold. Stick-thin, stiletto-wearing young women dressed to the nines even during daytime were in abundance and I rarely saw a young woman I'd deem a normal weight. A car sticker showing a high-heeled shoe, together with the warning “Woman Driver!” ceased to be amusing after we'd seen it repeatedly, and after one guide nonchalantly told us it was to ensure their safety!

On our last day on the Crimean peninsula, before heading back to Kiev, I decided to finally have a day on the sea, hiring one of the local fishing boats to take us out. It was a beautiful warm day and the calm Black Sea had a refreshing chill to it. The bay of Balaklava quickly disappeared from view as we sped along, giving way to a coast of craggy hills and verdant forests. Our boatman pointed to dolphins playing in the distance, though sadly I was never quick enough to spot them. Who would have suspected a nuclear submarine base was just round the corner? Or that this was where British troops spent a winter during the Crimean War, and when they were sent full-face woolly helmets, giving the balaclava its name? That was the magic of Ukraine, I thought. Beautiful, sometimes so familiar, and yet with a surprise and a story around every corner.

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