A couple of steps from the Fulgor is Piazza Ferrari, where, in 1989, gas company workers stumbled over the Surgeon’s House (Domus del Chirurgo), a well preserved second-century AD Roman villa, complete with beautiful mosaics and the most extensive collection of medical tools from the era discovered to date. Scrawled on a wall, archaeologists found the inscription “Eutyches homo bonus”, a patient’s review of the resident doctor’s work. Eutyches was, reportedly, a good operator.

Lunchtime in Rimini is piadina time, so we head towards the seafront and choose one of the many white-and-blue striped huts set up along the lungomare (beach promenade) in which the flatbread is cooked over a hotplate. The best of several fillings on offer is the most traditional: Parma ham, squacquerone (fresh local cheese) and rocket leaves. We follow that with a proper espresso in the luxurious setting of the nearby Grand Hotel, where, in terms of charm and glamour, the clock stopped in 1908, the year it was built.

As the afternoon fades into evening, the young and the fashionable flock to the waterfront, prepared for a long night, but we skip the clubbing and head inland, to Santarcangelo di Romagna.

The birthplace of Tonino Guerra, a poet and screenwriter much admired by Fellini and Michelangelo Antonioni, the village’s steep alleyways are crowned by the Rocca Malatestiana, a castle that is now the private domain of Princess Marina Colonna, from Naples. Climb up to it at this time of year and you’re likely to pass some of the young artists who gather from all over Europe to showcase their talents at the Santarcangelo dei Teatri contemporary performing arts festival (which started on Friday and continues until July 15). Residency programmes continue through­out the year, though the visiting artists sharing the village with the Mutoid Waste Company. Founded in London in 1980, the performance art group set up a caravan village/industrial sculpture park called Mutonia in the early 90s, on the banks of the Marecchia river, and have lived and worked here ever since.

The hike up to the rocca has built up an appetite that only Ristorante Zaghini and its signature fresh tagliatelle with beef ragu can satisfy. The fireplace opposite the restaurant’s main entrance is a reminder that snow often falls over the hills of Valmarecchia and Montefeltro in winter.

The following morning, we head south, past 18th-century villas that hide expansive private gardens and ancient trees, before crossing a bridge over the rocky bed of the Marecchia. As the road rises towards Verucchio, the green landscape is interrupted only by small, distant villages.

First settled as long as 3,000 years ago, Verucchio witnessed the sunset of the Etruscan civilisation (the artefacts the village’s Archeological Museum houses include amber and bronze orna­ments, clay pots, helmets and daggers, fabrics and, most impressive of all, a wooden throne decorated with human figures) before blossoming again during the Roman Empire and then gleaming with Renaissance splendour thanks to the Malatesta dynasty.

It is after that dynasty’s patriarch, Mastin Vecchio, that the restaurant inside Verucchio’s castle is named. Against its outer walls, a dozen bicycles await their riders, who are taking refreshment inside. Valmarecchia is criss-crossed by bicycle routes and is the venue for many amateur races during the summer. Numerous restaurants and lodgings here go out of their way to facilitate cyclists.

We take a detour from La Marecchiese to see another imposing edifice. In Montebello Castle, Azzurrina, the daughter of a 14th-century feudal lord, was kept hidden because she was an albino. Being born with white hair and clear glass-blue eyes was considered a mark of the devil and the girl’s mother dyed her hair with a pigment that, instead of turning them black, as intended, turned her locks light blue (azzurro, in Italian). In 1375, on June 21 – the summer solstice – Azzurrina disappeared while playing with a ball in the basement of the castle. She was never seen again but legend has it that every summer solstice, Azzurrina’s voice can be heard, a story that attracts ghost hunters from all around the world.

Glad it’s not June 21, we leave Montebello and proceed south.

San Leo is a dramatic, medieval village dominated by the castle in which alchemist and scoundrel Count Alessandro di Cagliostro met his end, in 1795. The well-preserved interiors of the largely intact castle allow visitors to step back in time to a period of violent, centuries-long struggles for supremacy. Our tour through musty, dusty corridors is suffocating, though, so it’s a relief to emerge, gasping for air, onto the large terrace, which seems suspended over the Valmarecchia valley.

Our final destination, Pennabilli, is gathered on top of the hills where Valmarecchia blends into Montefeltro, where Emilia-Romagna becomes sand­wiched by Tuscany and the Marche region. The village is renowned for its festivals and fairs, examples being Artisti in Piazza (dedicated to street artists) and Mostra Mercato dell’Antiquariato, an antiques market that in summer attracts sellers and buyers in their droves. It was also Guerra’s final home, the poet having envisioned grand designs for Pennabilli before he passed away, in 2012.

Now in his 80s, Gianni Giannini, a man who has brought some of Guerra’s designs into being, knows every pebble of Pennabilli and makes for a passionate guide as he takes us from the Forgotten Fruits Garden to the highest point of the village, where a familiar landscape opens up.

“Do you know La Gioconda,” asks Giannini, squinting into the distance. It’s easy to understand why da Vinci painted the landscape of Montefeltro we’re now gazing at behind the Mona Lisa: this mellow, touching panorama perfectly complements the mystery and the subtle beauty of the quintessential Italian Renaissance icon.