The train from Oulx to Turin was of the short regional variety, a multi-carriage railcar in reality, but very agreeable. And new, and spotless. Catherine and I were the only ones in our carriage, which initially made me think we'd accidentally settled into first class, until I realised there were no separate classes on the train, or people for that matter.

We wove our way along a sometimes windy track, through tunnels, alongside cliff faces, and - over to our left - an ever-changing vista of rocky hillsides, with dramatic outcrops, stone walls, tiny churches and the occasional statue of Mary, sometimes perched in an impossible-to-get-to location yet visible for miles around. Which was probably the point; Our Lady of the Mountains sees all, is always there, watching over us.

She watched our train go by, and I wondered idly if we'd been on a Virgin train whether we would have received an extra blessing.

It was a quick trip: at times we got up to 150 kph. I know this because the train company thoughtfully provided an on-board screen which told us our speed at any given time. Most of the journey was in the 80 to 100 kph bracket but occasionally we tried to break some records. Maybe Bugatti had gone into the rail transport business.

Being a regional rumbler the train stopped at numerous stations, and eventually terminated at Torino. By 1pm we were standing outside a nondescript steel door in Via di Suzza, a very short walk from the Porto Nuovo station. This was the Airbnb that Catherine had found us. Niccolo buzzed us in, we lugged Catherine's snowboard bag and the rest of our gear up three floors and were greeted with shy enthusiasm by the young man himself.

The apartment was lovely - bright, contemporary in furnishings - and unlike the one we'd stayed in at Sauze d'Oulx - came with everything necessary for an enjoyable (though brief in this case) stay. Such as washing-up liquid, cooking oil, and a coffee machine with a supply of pods. There was a lot more too, Niccolo showed us, left behind by other Airbnb-ers. He shook our hands and left us to it.

A quick check of our onwards bookings revealed that part of the next day's journey required us to physically print a ticket - an electronic version being unacceptable. Catherine and I debated what to do about that, and with the remains of the day, and decided a) to find a photocopy/fax bureau or Internet cafe to print the tickets, and b) to just wander around the city and see what we could see.

The ticket thing proved to be a bit of a mission and we covered about 50 square miles of central Turin before finally finding the place we were looking for, followed by a further half hour of gesticulation, Internet searching for the tickets, torturing the Italian language, and confirming for the Signora in charge that Britain deciding to leave the EU was a molto bene thing.

The sun was in its late afternoon hazy stage, casting a golden light over the warm stonework of Turin's buildings as we wandered aimlessly through this once-capital Italian town. We photographed shafts of light slanting through arcades, a leaf-covered bicycle (which is taking the 'green' thing to extremes), an old water fountain, arched ceilings, and lots of doors.

Turin has some magnificent wooden doors, usually double and very tall, presumably designed to give access to horse-drawn carriages of old. Many led to courtyards, some were firmly closed, hiding their secrets behind. Some were ornately carved, others plainer yet still elegant, and all gleamed as though polished that morning. Maybe they had been.

As we walked we found ourselves drawn to a very curious building standing out above all else, an architectural enigma that seemed to be part Eiffel Tower, part railway station roof and part town hall. It was like a child had taken three or four very different model buildings and piled them one on top of the other.

It turned out to be a museum, the Mole Antonelliana, though it had started off as a synagogue, but a series of changing owners and ambitions meant it never fulfilled its original purpose. Today it is one of Turin's top attractions, with a vertiginous lift that takes visitors up the vast central interior, past exhibition floors and up to a viewing gallery on top from which extensive views of Turin can be enjoyed.

Catherine elected to join the almost-hour long queue for the privilege of being hauled on high, while I decided to meander through more boulevards and back streets in the early spring warmth of the afternoon sun. When we met up later she raved about the interior of the museum, the ride to the top, and the fantastic views.

Between us we'd had an enjoyable afternoon without over-researching, following guide books or being told by Trip Advisor what we should see. Sometimes making it up as you go along is the best, as anyone who's done it knows. It's the clever person's key to discovery.

We are the Shrewd of Turin.