Arrive in Milan and transfer from Malpensa Airport to your hotel. There is no fixed sightseeing programme today, which suits a city that is best introduced without rushing at it. Milan is Italy at its most tailored, where Gothic stone and old courtyards sit comfortably beside fashion houses, trams and the sharp lines of the modern skyline.

By late afternoon, Milan begins thinking about aperitivo. The ritual has become part of the city's social grammar, giving you an excellent excuse to wander through Brera before taking a seat somewhere for a drink and small bites ahead of dinner. The Duomo and Galleria Vittorio Emanuele II are close enough for a first look at the city too. Nothing needs to be accomplished tonight. Italy has eleven days to make its case.

Leave Milan for a full-day excursion to Lake Como, where towns and villas occupy the narrow ground between mountains and water. A scenic cruise forms part of the experience, placing you out on the lake itself as gardens, wooded slopes and waterfront settlements pass along the shore. Como has drawn people seeking prettier surroundings since Roman times, and two thousand years have done little to weaken the argument.

Milan will feel decidedly urban again by evening. Head towards Navigli for dinner beside the canals, or return to Brera and look for a traditional Milanese menu. Risotto alla Milanese, coloured with saffron, belongs unmistakably to this part of Italy. One day into the journey, the regional differences are already beginning to show.

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Travel by train from Milan to Venice, where streets begin disappearing into water almost as soon as the city takes over. Later, board an included gondola ride and move through the canals beneath stone bridges and alongside palazzi whose front doors were designed with the water in mind. Venice spent centuries looking outward as a trading republic, and the wealth that returned through its lagoon shaped everything from its architecture to its appetite.

That trading past still turns up on the plate. Find a bacaro around Cannaregio or near Rialto and order a few cicchetti at the counter, the Venetian habit of pairing small bites with a glass of wine. Afterward, keep walking. Venice becomes particularly persuasive once the main squares fall behind and a succession of little bridges stops you caring whether you are taking the shortest route.

Leave Venice by train for Florence, arriving in the city that gave the Renaissance some of its greatest names. There is no fixed sightseeing programme after arrival, so the afternoon belongs to Florence itself. The historic centre is compact enough for the Arno, medieval streets, Renaissance façades and Brunelleschi's unmistakable dome to begin appearing almost immediately.

Tuscan cooking shares something with its architecture: confidence without much need for disguise. Around the centre, a piece of schiacciata, a bowl of ribollita or a simple gelato can be as revealing as an elaborate meal. Walk across Ponte Vecchio into Oltrarno, or climb to Piazzale Michelangelo towards sunset. Florence looks particularly composed from up there, even if the streets below rarely are.

Today the theme of Italia on a Plate arrives fully at the table. Travel through Tuscany to Siena and the Siena Cathedral, continue to the towered skyline of San Gimignano, and cross the vineyard country of Chianti before reaching Pisa. A traditional lunch with wine is included along the way, bringing together the landscape, produce and local table in the part of Italy where that relationship is hardest to miss.

Florence receives you again in the evening, but there is little reason to chase another checklist. Cross into Oltrarno and find your way towards Piazza Santo Spirito, where neighbourhood restaurants and outdoor tables take over as the day cools. Tuscany has already been generous.

Travel south by train to Naples, and Italy changes register almost immediately. Founded as Neapolis by the ancient Greeks, ruled and re-ruled for centuries afterward, Naples absorbed each layer without becoming particularly obedient to any of them. Balconies crowd above narrow streets, scooters find gaps that do not appear to exist, and everyday life seems to happen with very little separation between indoors and out.

Spaccanapoli and Via dei Tribunali make a natural introduction to the old city. They also bring you close to one of Naples' most famous contributions to the world. Pizza here is wonderfully uncomplicated on paper: dough, tomato, cheese, heat. Then an oven door opens, the crust blisters in seconds, another pizza lands on a plate, and the simplicity starts looking considerably more serious.

The Mediterranean takes over as you travel through Sorrento, Positano and Amalfi on a full-day coastal excursion. Sorrento sits high above the Bay of Naples, Positano seems to pour down the cliff towards the water, and Amalfi carries the memory of its maritime past. Part of the journey unfolds by boat, giving the coastline its proper scale from sea level.

Look above the road, and the famous Amalfi lemons often grow on terraces cut into the hillsides, their branches protected beneath pergolas. Citrus turns up everywhere here, in cakes, granita, sorbet and bottles of limoncello, because geography has a habit of finding its way into the kitchen. Back in Naples, the Quartieri Spagnoli provides a livelier change of scene. Washing hangs overhead, conversations travel between balconies, and dinner can take as long as it likes.

Cross the Bay of Naples for a day exploring Capri and Anacapri, moving between the island's busier centres, higher ground and wide Mediterranean viewpoints. The Blue Grotto is part of the booked programme when sea and local operating conditions allow. Capri once persuaded Emperor Tiberius to spend much of his later reign here, which says something about the island's powers of distraction.

The island has lent its name to dishes and flavours recognised far beyond the bay, but there is no need to turn the day into a tasting exercise. A coffee or lemon granita with the sea somewhere below can do the job perfectly well. Back in Naples, spend the last Campanian evening around Chiaia or Piazza del Plebiscito. Tomorrow, the south disappears behind the train window.

All roads lead to Rome, and this one finally does too. Travel north from Naples before entering the ancient city through the Colosseum, Roman Forum and Palatine Hill. These are names most travellers know long before reaching Italy, through emperors, gladiators, Caesar and the stories Rome left scattered through Western history. Here they stop being references and become walls, arches, roads and enormous pieces of stone beneath your feet.

Monti sits conveniently close for the evening, with small restaurants and tables tucked into lanes beside the ancient quarter. Roman food has its own rules and strong opinions, particularly when pasta is involved. Cacio e pepe, carbonara, gricia and amatriciana look deceptively simple until Romans begin discussing how each should actually be made. Some arguments are better investigated over dinner.

Rome widens beyond the ancient city today. A flexible hop-on hop-off tour allows you to move around the capital before entering Vatican City for the Vatican Museums and Sistine Chapel. The collections gathered here over generations move through sculpture, maps, tapestries and painted rooms before Michelangelo's ceiling brings almost everyone to the same temporary halt beneath it.

For the last full evening, take the streets towards Trastevere or the old Jewish Ghetto. The latter has shaped a distinct branch of Roman cooking, including dishes such as carciofi alla giudia, crisp-fried artichokes associated with the city's Jewish community. Rome has had thousands of years to accumulate layers. Some are preserved in museums, others are still being served at dinner.