Budapest has long been know as the Queen of the Danube. But it was the King of the Detectives who caught Andrew White's eye

You've got to love a city that erects a statue of television's shambolic Lieutenant Columbo for no obvious reason. As a fan of all things weird and wonderful, as soon as I found out that the good people of Budapest had recently done just that, the figure of the late, great actor Peter Falk became a "must see" for me during a week-long trip to the city. As usual, Falk didn't disappoint - and for me, he came to epitomise the quirky charm of the Hungarian capital.

Budapest, as most people know, is actually two cities for the price of one - Buda and Pest - separated by the wide expanse of the not-so-blue River Danube. The two are joined by several fine bridges, including the art nouveau Liberty Bridge, the three-way Margaret Bridge and the impressive Chain Bridge, flanked by four imposing stone lions.

Crossing the Chain Bridge - of which the locals are very proud - is almost compulsory for the tourist and heading over from the Pest side leads to the foot of the undulating Buda Hills. From here it is a short walk from the delightful Castle District, which can be accessed via a quaint wood-panelled funicular railway.

The district is dominated by the city's former Royal Palace, but that building is just one small element of an eclectic mix of interesting streets and buildings. Here you'll find the magnificently over-the-top Fisherman's Bastion, its glistening white turrets reminiscent of a Disney fairytale and which offers you one of the best panoramic views of the whole city.

I'd also recommend a walk around the creepy labyrinth – Budavári Labirintus – which burrows into the rock and where Vlad the Impaler is reputed to have been imprisoned - but this is most certainly not for the faint-hearted.

Still on the Buda side, the Cave Church - literally a castle carved into the rock - is well worth a visit, followed by an exhausting but rewarding walk up the winding path of Gellert Hill to see the Liberty Statue, which towers over the city.

Like most big cities, there are several unmissable landmarks. These include the magnificent Parliament Building, an imposing gothic vision reminiscent of our own, the elegant Matthias Church and Heroes Square, an iconic statue complex which also incorporates the Tomb of the Unknown Soldier. Darker days are recalled in the city's Holocaust Memorial Centre, which pays tribute to the Hungarian victims of Nazi rule - a brief but terrifying episode in the country's history, which this fascinating but harrowing museum captures in vivid detail.

For a change of pace, Margaret Island - it really is an island in the middle of the Danube - is a popular recreational spot for residents. And then there is City Park, with its thrilling zoo, which I wandered round with childlike wonder, rubbing shoulders with animals including buzzards, penguins, rhinos, giraffes - and a very cheeky orangutan.

Columbo aside, if it's statues you want, then take a trip to Memento Park, a veritable graveyard for the imposing statues of Lenin and his comrades which dominated the city squares and corners during the grim days of Communist rule. It is certainly worth getting off the beaten track to seek out less well-known attractions like Memento Park, and it is easy to explore Budapest using the much lauded underground system. Without this, I would certainly not have found the Hungarian Pinball Museum, which houses a dizzying display of vintage and modern arcade machines - and all available to play for a modest fee.

Speaking of money, my reviews of holiday destinations to friends usually start with the cost of alcohol, and in this regard Budapest is outstanding. An average £1.50 for a large (500ml) glass of the very good local beer is exceptional value - as is everything else in this fine city.

And if the beer is good, then the bars are phenomenal. Budapest is famous for its ruin bars, which have been established in abandoned buildings and furnished with rejected furniture and junk. They may look as dishevelled as Columbo's raincoat, but appearances are deceptive.

The most famous and best is Szimpla Kert, an Aladdin's Cave of a pub where you can even have a drink sitting in an old Trabant. This dilapidated building is full of delights, each dingy room crammed full of what was once trash - but which, in these hands, become real treasures.

In short, I love Budapest - and not just because of Peter Falk. It is a friendly, modern, vibrant, quirky and undeniable beautiful city and it is easy to see why it is becoming an increasingly popular destination.

Just one more more thing... I can't finish my review without mentioning my faultless home for the week, the Bo 18 Hotel. This little gem of a hotel is smart, modern and clean, with unfailingly polite and helpful staff - the free champagne for breakfast instantly making it one of my all-time favourites.

It may not be the most luxurious hotel I have ever stopped in, but it is certainly one of the best.