Laid out before me on the table is a smorgasbord of sweets the like of which I haven't seen in quite some time - crisp strudels filled with apples and plums, slices of chocolate-apricot Sachertorte, sweet pies with plums and soft cheese, a Bundt-type cake called gugelhupf and a specialty of this particular establishment, Sperl cake, rich with chocolate and nuts.
It is no secret that the Viennese are serious about their sweets but this spread provides edible proof.
Shared among our group, the cakes are gone in moments, much to the pleasure of our host, Manfred Staub.
A dapper gent with a twinkle in his eye, Mr Staub is the proprietor of Cafe Sperl, in Vienna's 6th district.
After opening in 1880, Cafe Sperl became popular with architects, artists, musicians, actors and singers as well as the military establishment.
It retains much of its old-world charm, with parquet flooring, timber panelling, big windows and ornate ceilings.
Mr Staub bought the coffee house in 1968 and has, we are told, worked here more or less every day since.
He's now an octogenarian but still comes in every morning, settling into one of the comfortable window seats with his paperwork.
His son Rainer has been working alongside him for the past eight years, covering the afternoons.
Rainer is, Mr Staub tells us in shaky English, "as old as the coffee house is mine".
The coffee house's old-fashioned elegance has proved attractive to filmmakers and it has appeared in movies including the 1995 romantic drama Before Sunrise.
More recently, the cafe appeared in A Dangerous Method as the setting for a meeting between Sigmund Freud and Carl Jung.
The film's director, David Cronenberg, was so impressed by its fin-de-siecle authenticity he told an interviewer "nothing had changed in there, except the cakes".
The coffee house appears for only a couple of minutes in the film but Mr Staub says it took a crew of 200 people three days to shoot.
Our cakes devoured, we turn our attention to coffee.
Most of us opt for a melange - a shot of espresso with foamy milk, a little like a cappuccino - but the options listed on the menu are extensive to the point of being slightly overwhelming.
The main ones to know are "brauner", which is black with a splash of cream and is available in "gross" (large) or "klein" (small), and "mocca" or "mokka", which is black coffee and quite different to the chocolatey mocha you'd order in an Australian cafe (which is called "intermezzo" here).
There is also a dizzying selection of coffees laced with alcohol, including the Maria Theresa, named for the famous Hapsburg empress, which contains orange liqueur.
It all comes out in the typical coffee-house style, on silver trays, with a teaspoon balanced on the top of the coffee cup and a little glass of water.
Sipping my melange, it is tempting to linger in Cafe Sperl - to make a selection from the array of newspapers and nestle into one of the plush booths for the rest of the day.
Indeed, lingering is pretty much Viennese coffee houses' raison d'etre.
Tourist attractions in themselves, coffee houses are as intimately associated with Vienna as Hapsburg-era imperial splendour or classical music.
Coffee was apparently introduced to the city by invading Turks in the 17th century and Vienna's first coffee house opened in 1685.
The end of the 19th century, when there were about 600 cafes in operation, is generally recognised as the peak of the phenomenon but it continues to be a part of daily life for Viennese people today - our tour guide Gerhard tells us he visits his local coffee house every day.
What sets Viennese coffee houses apart is the atmosphere of unhurried relaxation and contemplation - they are the polar opposite of Italian cafes, where patrons dash in and out for a quick shot of caffeine taken standing at the bar.
Gerhard compares them to an extended living room and tells us that, in the glory days of the coffee houses, many regulars would get their mail delivered to their favoured cafe.
Reflecting this, most coffee houses have long opening hours, from about 7am to midnight and beyond.
And while coffee house waiters have a reputation - frequently undeserved - for being grouchy, they are pretty much guaranteed to leave you well alone after taking your order, meaning you can sit in peace for as long as you please.
While at Cafe Sperl, one of our Austrian hosts tells me that Mr Staub's many years of hard work are not a rarity in the business, referring to one coffee house owner who worked right up until he died aged 100.
The coffee house in question is called Cafe Hawelka and is just a short distance from St Stephen's Cathedral in the city centre. The owner in question was Leopold Hawelka, the son of a shoemaker, who opened the cafe (his second) in 1939 with his wife Josefine.
The business closed during World War II when Leopold was called up for military service but reopened in the winter of 1945.
By the 1950s, it had become a popular meeting place for painters and writers; Henry and Arthur Miller and Andy Warhol all dropped by when they were in Vienna.
Josefine worked in the cafe, making her signature Buchteln every day until her death, aged 91, in 2005.
In his latter years, Leopold sat out the front to greet visitors. He died in 2011. The business is still run by the family and the couple's son Gunther has taken over his mother's baking.
I'd heard that Cafe Hawelka had become something of a tourist attraction as the late proprietors' fame had spread but when we arrive late on a midweek afternoon, it's peaceful and half-empty.
The lights are dim and the walls panelled with dark timber and hung with an eclectic selection of artworks (apparently Mr Hawelka was a great collector).
The whole place has a slightly dog-eared quality which feels comforting and relaxed. I'm reminded of Gerhard's words from Cafe Sperl - it certainly feels more akin to someone's oversized living room than a public cafe.
On my final day in Vienna, we visit one last coffee house, Cafe Pruckel, perched just inside the Ringstrasse, the ring road which encircles central Vienna.
I'd heard that Pruckel had a 1950s decor dating back to a refurbishment from that time. (The cafe itself is more than 100 years old.)
But rather than the US diner-style interior I had expected, this translates to a supremely elegant fit-out with a gentle touch of mid-20th century modernism - sleek chrome hat racks, space-age cone-shaped lampshades, vintage soft furnishings and a high ceiling painted with stripes of the cafe's signature salmon pink. Save for a scattering of patrons tapping away at laptops, it feels as though I've stepped back in time by 60 years.
It's a Saturday, so the coffee house is full of people, from an elderly man sitting by the window to a couple with their young daughter and clusters of well-dressed 20-somethings, perhaps students from the nearby University of Applied Arts.
It's lunchtime so we order food - an omelette with sausage for me - and sit chatting and people watching. It is supremely pleasant.
Eventually I have to take my leave as my flight home is looming.
But more than anything, I'd like to stay here, sipping a melange as the day glides gently by, lost in the coffee house rhythm of the rustling of newspapers and the murmur of quiet conversation.
Gemma Nisbet was a guest of the Vienna Tourist Board.
Cafe Sperl, Cafe Hawelka and Cafe Pruckel can be found online at cafesperl.at, hawelka.at and prueckel.at.
Hotel Sans Souci is a centrally located boutique luxury hotel in an historic building with interiors by Philippe Starck's design firm yoo. Rooms are from about $327 per night. sanssouci-wien.com.
For more information on visiting Vienna, go to vienna.info.