My coffee arrives on a silver platter courtesy of a waiter with a jaunty-angled bow tie and a surly attitude. Alongside it is a glass of water and two glistening cakes. Around me the hubbub and cutlery of a hundred tourists, all buzzing with caffeine, echoes through the marble columns and right up to the vaulted roof of Café Central. Outside the front door there's a 20-strong queue waiting to get a table.

Formerly Vienna's stock exchange, Café Central is one of Austria's oldest, most famous and most traditional coffee houses. According to the MD, Kay Fröhlich, it now buys almost four tonnes of coffee a year, and serves more than 380,000 cups, the lion's share to tourists. Sullen waiters (it's all part of the act) in dickie bows have been serving coffee much like this for the last century and a half. Former customers include Leon Trotsky and Vladimir Lenin who, in between their mélanges (that's a Viennese coffee similar to a cappuccino), plotted overthrowing the Russian tsar here. Witness the power of caffeine.

Now on my third double espresso (or brauner grosser) of the day, I'm feeling the power of the bean myself. Earlier in the morning I'd been in the north of the city, near the university district, at another café called Coffee Pirates. But that had been an altogether different experience – part of what's known as Vienna's third wave of coffee houses, and diametrically opposed to traditional coffee houses in pretty much every imaginable way.

Where Café Central has uniformed waiters, laminated menus, Thonet No.14 bistro chairs and button-operated coffee machines, Coffee Pirates has hipster baristas, a chalkboard menu that changes daily, its own roaster, and – obviously – a Dutch coffee machine that "had to be ordered six months before it was delivered and cost more than a family car".

80% of Café Central clientele are international tourists, while at Coffee Pirates it's almost exclusively students from the University of Vienna campuses across the road. All the staff wear hats, but cool hats with a certain individuality. In an obvious inversion of Vienna's traditional coffee house, a dozen or so Thonet chairs have been nailed upside down to the ceiling.

The owners of Coffee Pirates are Werner Savernik and Evelyn Priesch. "Yes, the traditional coffee houses are really nice," says Evelyn, careful not to disrespect her old-school rivals in the centre of town. "They have great furniture and lamps and newspapers. But, to be honest, the coffee is not very good. They focus on everything but the coffee. It's mainly a tourist thing. Locals don't go there."

Essential Viennese coffees

Advocaat: coffee, egg liqueur and cream.
Brauner Kleiner: single espresso.
Brauner Grosser: double espresso.
Einspänner: double espresso in a glass topped with whipped cream.
Kaffee verkehrt: more milk than coffee, similar to a latte macchiato.
Kapuziner: cappuccino.
Maria Theresia: double espresso and orange liqueur, topped with whipped cream.
Melange: a classic Viennese coffee with lots of steamed milk and milk foam on top, similar to a cappuccino.
Mokka: a slowly extracted espresso.
Obermayer: an espresso with chilled cream decanted via the back of a spoon.
Pharisäer: coffee, rum and cream.
Türkischer: ground coffee and sugar are boiled with water and served in a pot.
Uberstürzter Neumann: whipped cream served on a double espresso.
Verlängerter: an espresso with hot water added and milk or cream on the side.
Wiener Eiskaffee: chilled coffee, vanilla ice cream and whipped cream.

Her establishment, with its rustic interior, sacks of coffee piled high, little roastery in the back and student-y clientele, very much puts the bean first. Evelyn claims to know every farm in the coffee belt that supplies her with raw material. "We've just got back from visiting one farm in Ethiopia," she says. "For us, coffee is a hobby as well as a job. We're not doing this just for the money." She and Walter are surfers. When they go on holiday they head for tropical countries where they can ride the waves at the beach and sample coffee in the nearby mountains. Kenya is a particular favourite for this unlikely saltwater-caffeine combo.

As Evelyn shows me the basics of her roasting machine, and while I sip on a filter blend of Panamanian, Honduran and Ethiopian beans, she admits that her café does in fact share a few old-school qualities with the traditional coffee houses found in the centre of town. Regular customers while away hours in here, reading, writing, and meeting new acquaintances. Two published books she knows about have been drafted here. And several romances have flourished. One couple who first met across Evelyn's coffee cups have since produced a baby. Throughout the entire café there pervades a sense of what the Viennese call gemütlichkeit.

There's no direct translation for this German word. It describes a state of cosiness, warmth, friendliness, belonging, peace of mind, even social acceptance. "To achieve gemütlichkeit, you drink a long coffee, you spend time in the café, you slow things down, relax and appreciate life," Evelyn explains. "You might read the newspaper, talk to someone or daydream."

Viennese coffee and its accompanying gemutlichkeit dates all the way back to the late 17th century and owes its development to an Armenian merchant called Johannes Diodato who first imported coffee to the city from Turkey. (There's also a legend about a chap called Kulczycki who appropriated sacks of coffee left behind by retreating Turks after the Battle of Vienna in 1683, but scholars later proved this isn't true.) Over the next three centuries the city's coffee houses flourished.

Frequented by writers, musicians, artists and intellectuals, they grew into the established institutions they are today. "In Vienna, the pleasures of coffee have become the hallmark of an advanced civilisation," write Werner Meisinger and Rudolf Novak in their book Café Central: Viennese Culinary Culture Then and Now. Local writer Hans Weigel goes even further: "It's as if it has become part of the people's soul." According to Vienna City Administration, there are now around 2,500 businesses across Vienna serving coffee, comprising 900 traditional coffee houses, 800 café restaurants, 680 espresso bars and 120 café-confectionaries.

Quite what category the next café on my tour comes under is anyone's guess. Called Supersense, it's honestly the most unusual coffee house I've ever visited. At the back of the building, past the actual café area, things start to get very surreal indeed. There's a 200-year-old printing press, a studio camera from the 1930s, a record lathe from the 1950s, and an old Voice-O-Graph recording studio the size of a telephone box – all restored to working order.

Supersense is a paean to all things analogue. Dotted around the shop are examples of cultural artefacts from a pre-digital age: Polaroid film, hand-printed greetings and business cards, limited-run vinyl records, obsolete music formats, antique stereos, TV sets and musical instruments. The owner is Florian Kaps, an evangelist for all things analogue. In a world dominated by digital technology, he sees himself as a kind of mechanical conservationist saving defunct analogue machines from extinction. He has already revived the production of Polaroid cameras and film, and he's now got his eye on the world's few remaining typewriter factories.

"I'm fighting my arse off," he says. "If there weren't crazy people like me rescuing these technologies, they'd be gone forever. So I'm connecting these endangered technologies to the younger generation."

And where does the café come in? Well, Florian uses his artisanal coffee to invigorate his customers' sense of taste before they then exercise their other senses through the analogue technology. "Eating and drinking are the easiest ways to access the human senses," he says, adding that the building he occupies used to be a traditional coffee house. "Without our café, people would look at Supersense and ask: 'What is this? A church? A museum?' They wouldn't understand the rest of it."

Easier to comprehend is the final café on my tour of Vienna. Kaffemik is a tiny six-seat establishment over in the trendy Neubau district. The boss is Simon Huber, who sources his beans from roasteries all over Europe. Despite the size of his café, he serves 35,000 flat whites a year.

By now, the levels of caffeine in my bloodstream are distressingly high. My hands are shaking, I've got a pain behind the eyes and I'm talking 19 to the dozen.

"Don't worry. I drink six to eight shots of coffee a day," Simon says, as if that's the most normal thing in the world. "But it's under control. The only problem is, if I don't have a coffee at night, when I wake up the next morning I have caffeine withdrawal." And to think that I'd been worrying about my caffeine addiction…

Dominic Bliss was a guest of the Austrian and Vienna tourist boards. austria.info; vienna.info. He stayed at The Guesthouse Vienna. theguesthouse.at