I’ve never been to Paris before, but it’s living up to its reputation so far. I only arrived a few minutes ago and have parked myself in a posh 1920s-style cafe across the road from Gare du Nord, where the Eurostar train deposits Channel-hoppers like me.

I’m here to begin a three-week grand tour across the continent: from Paris to Naples via Nice, Florence and Rome. I’ve never travelled to mainland Europe before. I haven’t been able to afford it, and even if I’d had the money, anxiety would have kept me home as I suffer from mild travel phobia. So, as well as a holiday, this trip will also be a sort of aversion therapy.

At the ingeniously named Café du Nord, a waiter in a black waistcoat, bow tie and beret brings my café au lait and croque monsieur on a small round tray, then departs with a nod and a “bon appetit”. It’s all very elegant. I eat, drink, tip, wave au revoir and leave for my hotel, a budget affair near the Bastille.

I only have three days in Paris, and intend to make the most of it. Some Parisians claim the best thing to do in the city is become a flâneur and wander aimlessly. But that whole concept could describe my life thus far, so I decide to see the sights.

I grudgingly board an open-top bus tour. When I lived in London, I used to deride the gawping day trippers who’d view the city one monument at a time through tiny rectangles. But it’s a good way to see an unfamiliar city and get a potted history via the complimentary earphone commentary.

I also visit the Eiffel Tower: it’s just like Blackpool Tower only bigger, and in France. Then I go to see the Mona Lisa in the Louvre – it’s all right, but I don’t really see what all the fuss is about. Tomorrow I leave for Nice.

The first part of the train journey to Nice is through scorched farmland, but after departing Marseille it takes in spectacular vistas of the French Riviera. To my left, misty mountains fill the horizon, lush vineyards lie trackside, and sandy-walled villas with sun-kissed copper roofs pepper verdant hillsides. On my right, there are clusters of exotic trees – palm, pine and olive. Beyond them is the Mediterranean, shimmering in the sun. I have to pinch myself: all this distance and beauty for less than £50.

Nice is nice, but that’s as far as it goes. Again, the bus tour is worth doing, but the old town is the thing to see: a collection of pretty buildings where you can spend a fortune in a pretty cafe on a pretty alleyway and look at statues perched in the middle of marble fountains. I then head to the Promenade des Anglais where there are ice-creams, surfing and other coastal pastimes on its pebbled beach.

If you’re fair-skinned like me, the big drawback about visiting the continent in August is that it’s baking hot. I end up looking like a soggy sundried tomato, which is more demoralising than usual given the number of olive-skinned beauties waltzing about in shorts and vests.

I’m supposed to be heading to Italy, but I’ve left my phone in the taxi I took to the train station. These days losing your phone is like losing a limb, so I’m panicking and considering visiting the British consulate and calling this whole thing off.

On the Find Me app on my laptop I watch my phone do circles of nearby Monte Carlo. I resolve to get another cab and instruct the driver to follow my phone icon. Unfortunately, the app is unreliable, so I return to the station and somehow contact Uber and the driver, who returns my phone hours later. That’s five hours of my life and £200 I’m never getting back, but finally I board the train to Genoa, and from there change to another heading south into the Tuscan hills.

“Ahh, Florence,” I hear myself say more than once as I gaze at the opulent architecture, romantic streets and renaissance art. I feel genuinely emotional when I set eyes on the Piazza del Duomo and Florence’s 14th-century cathedral.

The joy is sapped slightly by the roving groups of tourists. I’m a hypocrite, of course, because I’m one of them. Central Florence, at least when I visit, feels like an estate agent has curated it. It’s spotless, and boy are you being sold something. That something being a version of Italy seen through the lens of a Dolmio ad. The restaurants play the Godfather soundtrack on a loop and serve pizza, pasta, gelato and more pizza. At one restaurant, a slight man wanders up, sets an amp down and mimes to Pavarotti, wild gesticulations and all.

My next stop is Rome. It’s an ethereal place. It feels as if I’m being ambushed by history – ancient fountains, the Colosseum and the Spanish Steps – with manicured cypresses, broad umbrella pines and lush palm trees appearing around corners with no warning.

The best way to see Rome is on an electric scooter in the early hours of the morning. I whiz around empty cobbled streets, and the city’s landmarks look even more dramatic lit up.

The one thing I have to see in Rome is the Sistine Chapel. To gaze up at Michelangelo’s ceiling, I have to buy a ticket for the Vatican Museum, and like many museums and tourist attractions on this trip, that had to be arranged through an unnecessary middleman. This involves visiting a tobacconist a few metres from the museum, where a tour guide picks me up, walks me to the museum entrance, hands over the tickets, then leaves. (I later learn that I could have booked a slot online.)

I walk through several galleries on the way to Michelangelo’s masterpiece, but they’re more than worth it. The gallery of maps is spectacular – with its gilded vaulted ceiling and gorgeous frescoes. Painted topographical maps inspired by Ignazio Danti’s drawings decorate the walls and giant windows offer stunning views of the city.

I finally get to the main event. It’s serious here. No photos, no shorts or vests, and the Vatican demands silence, which of course, everyone ignores. The ceiling is an awesome feat, but I find the paintings disturbing. Many frescoes depict suffering and trauma; an entire wall shows demons dragging naked people to hell on one side, and angels carrying people to heaven on the other. Also, it’s impossible to experience the chapel as Michelangelo intended – recumbent and in silence – because the place is heaving, and security can’t wait to get you out again.

I had planned to end my trip with a few days in Naples – for the pizza and ice-cream. But as that’s all I have eaten since arriving in Italy, I decide not to go on south. If you’re interested, the best pizza I had was at Mister Pizza, next to the cathedral in Florence. And the best ice-cream was in Via del Boschetto, a trendy street near the Colosseum in Rome.

This was a stressful journey for me but I’m glad I did it. In fact, I wish I’d had the courage to do this years ago.

Way to go

Getting there
Crossing the Channel on Eurostar costs from £69 one-way, Paris to Nice costs from €55, Nice to Genoa from €19, Genoa to Florence from €19 and Florence to Rome from €15.

Stay
In Florence, Casa Regina Santo Rosario (single rooms from €50 B&B) is a convent guesthouse where rooms are small and facilities shared, but it has a gorgeous garden, is very clean and quiet, and the nuns are friendly.

In Rome II Covo B&B (doubles from €90 B&B) is near the Colosseum and has high ceilings, opulent decor and a roof garden.

Eat
In Paris I enjoyed the best Greek food I’ve ever had at La Maison de Gyros near the river in the Latin Quarter. The souvlaki (€6 with chips) was delicious and the interior is all higgledy-piggledy chairs and tables, barmy artwork, books and other ornaments.

In Florence I loved the pizzas (from €8.50) at Mister Pizza and ravioli (€12) and lager at Le Botteghe di Donatello, both near the cathedral.

If you thought you’d eaten every pizza topping going, check out the daily changing menu of takeaway slices at Bonci Pizzarium near the Vatican in Rome. There could be cod and potato pizza, or pumpkin puree and octopus, all from €4 a slice.