We fell in love with Turin at a glove shop. We were following a walking tour in Eugenia Bell’s excellent Civilized Traveller’s Guide to Turin when we spied Moda del Guanto. The glove store’s old-fashioned cases of drawers stacked high behind counters drew us in.

It’s hard to find men’s leather gloves in good colours. When the sisters who own the shop pulled out a chartreuse pair with orange fourchettes, we started to tremble.

Soon they’d unloaded every drawer. Their designs were fresh; their work was perfection; their pride was clear; but what really charmed us was their sweetness.

Italians will tell you that Turin (or Torino), the capital of Piedmont in the far north-west and the home of Fiat, is a cold city, grey and industrial. When we were there it was sunny and warm, and so was everyone we met.

At the sleekly futuristic Baricole – Turinese for “eyeglasses” – I went through approximately 10 000 innovative frames before finding the perfect pair. The salespeople behaved as though they were delighted.

I was only sorry my face didn’t go with the pair whose temples were embossed with the city skyline, recognisable at once from the towering form of the Mole Antonelliana.

The Mole, Turin’s weirdest building, was begun as a synagogue in 1863, then given to the city. Today it houses the splendid Museo Nazionale del Cinema.

The first part covers the medium’s pre-history – shadow puppets, magic lanterns and other such devices. Everything’s interactive, so it feels more like being in an arcade than like having an educational experience.

The second part is a riot of posters, memorabilia (Fellini’s hat and scarf) and scores of clips. You can recline next to strangers on a rather decadent round sofa and watch love scenes projected overhead. Or, from a sea of chaise longues in the cavernous main hall, each fitted with its own speakers, you can lose yourself in the dreamy images on two movie-palace size screens.

Turin is, in fact, a city of museums. The much-loved Museo Egizio has so many statues of the lion-headed goddess Sekhmet that it sometimes feels like a zoo.

Currently the masterpieces of the Galleria Sabauda are being moved into a new setting in the Royal Palace, so only the greatest hits are on view. What a stroke of luck: no hunting around corners for van Eyck’s St Francis Receiving the Stigmata or Gentileschi’s Annunciation.

Turin, where vermouth was invented in 1786, is also a city of cafes. The Caffe San Carlo (opened in 1842) and the Caffe Torino (opened in 1903) are like two elaborately overdressed streetwalkers competing for clients on the enormous Piazza San Carlo: they may be ageing and expensive, but they still know how to deliver the goods.

There’s a finer view from the tables in front of Pepino on the Piazza Carignano.