Entering Central Kavehaz in downtown Budapest, I'm hit by a fragrant gust of espresso. Then a white-shirted, red-tied waiter with a bald head and a neat goatee says "good morning", and ushers me in to what feels like a different century.

We shuffle beneath high, lavishly decorated ceilings adorned with hanging brass lamps, passing a wooden coat stand, a rack fluttering with newspapers and a cluster of brown and maroon leather-backed armchairs. With the heady caffeine scent still swirling up my nose, I'm seated  at a marble-capped table beside a large window on which is etched  "Central 1887".

Founded that year, then lovingly restored by Hungarian millionaire Imre Somodyt at the turn of this millennium, Central Kavehaz is a legend on the Budapestian coffeehouse circuit, and an enchanting spot in which to kick-start the day (the ideal place to wake up and smell the coffee, you could say).

Although "black gold" has been imbibed in the Hungarian capital since the 16th century - when it was brought in the sack-loads by Ottoman Turkish invaders - kavehaz, or coffee house, culture really thrived here during the latter years of the Austro-Hungarian Empire, pre-World War I.  About 600 caffeine-fuelled establishments did a roaring trade across a metropolis melded by the merging of Buda and Pest, the neighbouring cities facing one another over the River Danube.

Like their famous Viennese counterparts, which drew characters as varied as Sigmund Freud, Gustav Klimt, Leon Trotsky and Adolf Hitler, Budapest's coffee houses lured a cross-section of society. Renowned for their egalitarian, smoky atmosphere, they were ideal for lounging and lingering; for discussing and dissecting current affairs; for plotting, perusing and people-watching. For avoiding the chores of real life. For daydreaming. These timeless pleasures endure.

As I nurse a cappuccino (whose frothy top is marked with a heart shape), and devour a crunchy croissant served with Nutella-esque chocolate sauce, I scan my fellow breakfasters.

Over the din of clattering cutlery emanating from the kitchen, I hear whispering Magyar (the Hungarian language) from a nearby table, where two attractive, well-dressed ladies in their late 30s eye each other intensely. Two French tourists - who can't stop snapping photographs of the antiquated decor - are seated next to a table of big-bellied besuited Hungarian businessmen. A Russian couple are next in. Then three Germans. Then two British. The bald waiter proves to be a paragon of multi-lingual efficiency.

I'm disappointed not to see any dandyish, beard-stroking intellectuals mired in impassioned debate, or tortured geniuses feverishly jotting down words or sketches. Artists, poets and writers once flocked to Central Kavehaz,and the late Hungarian author Csemer Geza - who died in 2012 - apparently had a table perpetually reserved for him, so he could work here.

Perhaps the bohemians will come later. Housed on the bottom floor of a graceful five-storey building, Central Kavehaz is open until midnight; its menu featuring cocktails, wines and spirits, as well as other caffeinated drinks. Its food section sports traditional Austro-Hungarian fare like goulash and boiled wienerwurst with mustard and horseradish.

Then there are the desserts. A chilled glass cabinet stocks an array of colourful, calorific temptations, which I try to resist. And succeed in doing so. Well, sort of.

A little later, having admired some of Budapest's grandiose architecture (including the daunting St Stephen's Basilica), it's time for another caffeine jolt. And some dobosh.

Whereas Vienna excels in the richly chocolate sachertorte (invented by Austrian Franz Sacher in 1832), Budapest's iconic staple is the dobostorte. Also known as dobosh, this moist, multi-layered medley of sponge cake, buttercream chocolate and caramel was created in 1885 by Hungarian confectioner Jozsef Dobos. Austro-Hungarian emperor Franz Joseph I and his Empress Elisabeth were among the first people to sample it.

I have a scrumptious slice, with another perky cappuccino, from the shaded front terrace of Muvesz Kavehaz, a cafe established in 1898 on leafy Andrassy Avenue. Dubbed the "Budapestian Champs-Elysses", Andrassy is lined with elegant old mansions housing upmarket fashion stores, restaurants and cafes.

Facing the Hungarian State Opera House, Muvesz Kavehaz - which translates to Artist Cafe - is a fine alfresco spot, but its interior is breath-taking. Greedily inhaling the wafting espresso fumes, I survey the cafe's glittering chandeliers, antique paintings and black and white framed photographs of famous Hungarians, and, for a moment, think I spot Sigmund Freud. But no. It's just his spitting image  sitting  at a table studded with red lamps, sipping coffee with a buxom young woman, next to a group of Japanese tourists, who are silently scoffing plates of dobosh near a voluble gang of fur-hatted Hungarian grannies.

After a lovely mid-afternoon's amble along the banks of the Danube, I reckon I have space for one more coffee and cake.

Budapest has an impressive new wave of cafes, with hip baristas, eclectic furniture and walls splattered with political slogans and multi-coloured murals. But I can't resist the city's aging dames. The only dilemma is which one to choose.

Scouring my map, which I've earmarked with possibilities, there's Cafe Gerbeaud on Vorosmarty ter, one of the city's busiest squares, a minute's walk from the Danube. Dating back to 1858, it's famed for its delectable decor (think: marble, exotic woods and gold, stucco ceilings and chandeliers) and sweet-tooth temptresses like konyakos meggy (cognac cherry bonbons).

Rivalling Gerbeaud for opulence - and high prices - the palatial New York Cafe was the haunt of choice for much of the literati at the turn of the 20th century. After spells in the doldrums and closures, it was revamped and reopened in 2006. Blessed with flamboyant frescoes and gilded stucco columns, it shoulders the five-star Boscolo Hotel on the tram-lined Erzsebet Korut.

Founded in 1885, Muzeum Kavehaz annexes the Hungarian National Museum, and sits opposite a string of second-hand bookstores, some of whose contents, I fancy, were cobbled together in the city's coffee dens. Another option, Hadik Kavehaz, is a revived old-world cafe within easy reach of the city's soak-tastic Gellert Baths.

Mulling things over, I tell myself: whatever I miss today I'll check out next time.

It's my fourth trip to Budapest, and I've come to  realise that this city  has a knack of rewarding return visitors. Especially those with a weakness for coffee and cake.

TRIP NOTES

MORE INFORMATION

gotohungary.com.

GETTING THERE

Emirates fly from Sydney and Melbourne to Budapest via Dubai with return fares from $1550. See emirates.com

STAYING THERE

Rooms at the revamped five-star Kempinski Hotel Corvinus start at $157.  The hotel shares a building with Nobu Budapest;  the slick, informal ES Bisztro, which serves typical Austrian and Hungarian dishes (such as veal tongue stew with bread dumplings); and The Living Room, a modern take on the bygone Budapestian coffeehouse. See kempinski.com/budapest.