Start by taking the Siklo – a funicular railway built in 1870 – from its base at the historic Chain Bridge up to the Royal Palace.

Now you’re on Castle Hill, a 1km limestone slab towering 160m above the Danube. Home to enough museums and monuments to make it well-deserving of its Unesco World Heritage status, this isn’t a place to rush through.

Don’t forget to check out the Buda Castle Labyrinth – a 1200m cave system underneath the Castle District. You can also swing by the 500-year-old Matthias Church and, of course, the Royal Palace itself, which is home to the Hungarian National Gallery, the Budapest History Museum, and restored palace rooms dating back to the 15th century.

Pest

Pest is the younger, hipper sibling to the more mature, conservative Buda. There’s a distinctly urban feel on this side of the Danube, and you’ll find great shopping, plenty of trendy bars and hip pavement cafés. Check out Váci utca, the posh, pedestrianised main shopping street, for the best boutiques.

If strolling is your thing, go for an amble along the Dana korzo, a promenade that runs beside the Danube between Elizabeth Bridge and the Chain Bridge. It’s lined with restaurants, bars and craft stalls, and you’ll be serenaded by musicians as you go by.

Budapest spas

Strip off, wade in and kick back, and you’ll soon understand why Hungarians seem to be obsessed with ‘taking the waters’.

Budapest sits on a geological fault, which explains the 120 thermal springs bubbling up every way you turn.

There are a range of spa options, from the art nouveau Gellért Baths in Buda to the impressive (and massive) Szechenyi Baths at the northern end of City Park in Pest.

There’s a different procedure for each of the baths, but you’ll soon get the hang of how it’s done. Wear swimmers and take a pair of flip-flops along with you.

Budapest history

Smack bang in the middle of Europe, Hungary has experienced more than its fair share of 20th century vicissitudes – especially in relation to its Jewish history.

Budapest once boasted a thriving Jewish population, but after the Nazi occupation in World War II some 430,000 Jews were deported to Auschwitz, where the majority died.

The Moorish-style Great Synagogue in Pest is the world’s largest outside of New York. Go there to marvel at the ornate interior, visit the museum, and spend a few solemn minutes at the Holocaust memorial. The guided tours in English are well worth the small fee.

Budapest festivals

As the weather warms up, so too does the cultural life of Budapest.

The city’s festival season launches with the Spring Festival (March 20-April 3), a showcase of classical music with an accompanying Fringe Festival running from April 3-5.

By May 1 the pavement cafés of Pest start to open, and from mid-June a month of weekend entertainment – known as Summer On The Chain Bridge – begins on the eponymous crossing between the cities of Buda and Pest.

Finally all the action winds down with the Budapest Autumn Festival, which runs from October 10-19.

See festivalcity.hu for more information.

» Samantha Baden travelled with Ryanair and Hungarian National Tourist Office (020 7823 0411).