Which city in Europe would you say has the best squares and cafes

That's a completely impossible question to answer. I do hope that it's not the basis you'll use for selecting a city to visit.

Most big cities have lots of both.

Rome

Best on what basis?

How many?

How large?

Most beautiful?

Or by what other measure?

Generally more in number in more southern areas and fewer in more northern/colder areas - but almost every place I have been has charming squares.

Lots of them have good ones, so there is no one best city IMO.

Siena. Anyone who disagrees is a rube.

Ironically, the cafés on the most prominent squares (e.g. San Marco in Venice, Piazza Navona in Rome, Plaza Mayor in Madrid, Place Vosges in Paris) are generally overpriced, have rude service and poor quality. The reason is that the tourists congregate there and no local would ever go there. A menu in four languages with photographed items is a sure indicator for overpriced factory food.

The best squares are those which you discover when exploring a city on foot, including the back neighbourhoods.

The best squares are those which you discover when exploring a city on foot, including the back neighbourhoods.>

Venice is fab for that!

Let me throw in Rynek in Wroclaw. Unlike the others mentioned so far, not yet ruined by mass tourism but still frequented by locals just as well as visitors, and not overpriced.