A holiday in Ukraine? It seems unlikely at first, thanks to the bad press the country gets.

But with visa-free travel and direct flights from the UK, not to mention being remarkably good value, the country is opening up to tourism.

Although there are still skirmishes on its eastern borders, the rest of the country shows no signs of the conflict, while news reports about anti-Semitism seem limited to a couple of maverick politicians.

My own starting point of Lviv is in the far west, just 50 miles from the Polish border, known as the Paris of the East when it was part of the Austro-Hungarian Empire.

With its quaint cobbled streets and proliferation of churches, its architecture is similar to those other great Habsburg cities like Vienna and Budapest — the view from the 65 metre high Town Hall tower is worth every step to drink in the panorama.

Of course it also has trams, trolley buses and coffee houses. Indeed they say that the first coffee shop in Vienna was opened by a Ukrainian from Lviv in 1686.

With street musicians on every corner, it’s a pleasant place to wander round, Renaissance houses lining the Market Square in the old town.

My visit coincides with National Embroidered Blouse Day so everyone is sporting one, men and women alike, and there are demonstrations of folk dancing.

And inside the elaborate Lviv Opera House, there’s more dancing to be found, with productions of ballet as well as opera staged here.

Once the city’s old Jewish quarter stood just a short stroll south of here. A Renaissance entrance is all that remains of the late 16th century Golden Rose synagogue — destroyed by the Nazis after they invaded Lviv in 1941.

Around 136,000 Jews perished in the ghetto during their three-year occupation, and nearly 350,000 in nearby concentration camps.

Last year, both they and the history of Jews in Lviv were commemorated by a new memorial unveiled on the site.

Called the Space of Synagogues, and preserving some of the original foundations, it consists of a number of black stone slabs engraved with photos and quotes from famous Jewish residents.

But fascinating though this city is, it was only the start of what Ukraine has to uncover. Heading south and east, the flat wheat fields stretch for miles, but I soon started to climb into the Carpathian Mountains.

The region is home to the Hutsuls, an ethnic group who’ve been here for centuries, and whose lifestyle remains unchanged over the years.

In Kolomyia, a museum displays their colourful costumes and ornate arts and crafts — as well as being a place to pick up bargain souvenirs. If you have the time, don’t miss the collection of decorated eggs from around the globe in the world’s only Easter Egg Museum.

Leaving the mountains I come to the city of Chernivtski, capital of the region of Bukovina. Here, it’s only 30 miles from Romania and briefly, between the wars, became part of that country.

The Romanians were responsible for the city’s attractive Art Nouveau buildings but also for some of the worst Jewish atrocities.

Today an excellent museum in the former Jewish National House has a detailed chronicle of Jewish life in the city between 1774 and 1941. Chernivtsi’s former synagogue, famous for its exotic Eastern style, has now been converted into a cinema.

The countryside around bristles with fairy-tale fortresses. At Khotyn, a day trip from Chernivtsi, one sits on a cliff overlooking the Dniester River.

Built around 1400 by the Moldavians, it fell into Turkish hands in 1713 before the Russians became its new owners a hundred years later.

These days it’s been much restored but it’s still impressive, with walls 40 metres high and six metres thick. It’s been the location for many feature films, including the Ukrainian version of Robin Hood.

Nearby, at Kamyanets-Podilsky, another stunning fortress was built to defend the medieval city occupying an island in a bend of the Smotrych River.

The 14th century castle sits high above the steep canyon walls with the river acting as a natural moat. Nine towers of all shapes and sizes are linked by sturdy walls, enclosing a vast courtyard where the townsfolk could take refuge.

The picturesque streets of the old city hide a much darker past; used as a Jewish ghetto by the Germans during the Second World War, an estimated 30,000 people died. Today memorials stand here too, commemorating those who were killed.

As the sun sets, I travel east once more, on an overnight train to the capital Kiev. Slow but comfortable, the fading East German carriages lend the journey a certain Communist charm.

There are relatively few of those dull Soviet architectural monstrosities often found once we arrive, with onion-domed churches rising above the city’s wide leafy boulevards.

Since Ukraine’s independence many of the buildings have been restored and repainted as symbols of national pride.

The 11th century Orthodox cathedral of St Sophia sits minutes from the 1980s reconstruction of the Golden Gates of Kiev, while the striking 19th century St Volodymyr’s cathedral became a museum of atheism during Soviet times.

The city’s biggest attraction is the Lavra Cave Monastery, a complex of religious buildings with catacombs below containing mummified bodies of former monks.

More recognisable to most though is the Maidan Nezalezhnosti, the central square of the city and the venue for pro-democracy demonstrations in recent years.

Over 100 demonstrators were killed by snipers in February 2014 and, as a result, President Viktor Yanukovych fled the country, with his trial for treason now taking place in his absence.

These days, as if to emphasise the struggle is ongoing, the slogan “Freedom is Our Religion” is emblazoned in large letters on a sign dominating the square.

On the outskirts of town, another grim reminder recalls more Nazi atrocities here, at the Babi Yar monument. On 29 September 1941, Kiev’s entire Jewish population, numbering around 34,000, were marched to the ravine and massacred.

For the next two years, it functioned as a concentration camp with an estimated 100,000 people buried on the site.

These days it’s an eerie public park and among the various memorials here, the monument to Jewish children who perished is particularly moving.

A tragedy of a different sort became a byword for nuclear disaster, at Chernobyl, two hour’s drive from the city.

The world’s biggest nuclear accident in 1986, the site is now becoming a tourist attraction itself, with guided day trips showing news reports of the disaster — and equipping visitors with a personal Geiger counter before entering the 10 kilometre exclusion zone.

The reactor now has a new shiny metal shell, but the town of Pripyat, once housing 50,000 workers, is slowly being swallowed by the forest. A sort of modern-day Marie Celeste, it’s a chilling warning of nuclear power gone wrong — but a fascinating place to see.

And despite Ukraine’s often unhappy history, that’s something which is true of the country itself.