travelling throughout Italy

I think anything would work short of being bare foot. I have for years traveled in a urban hiking shoe from ECCO. It is a smooth toe, oxford style shoe with a heavy lugged sole called City Walker. It works because the heavy sole provides of a lot of cushioning between me and the cobble stones. It is also water proof -- not water resistant.

It really doesn’t matter, whatever you are comfortable in for walking on cobblestones. I (female) wear sneakers and take along a pair of sandals as slightly dressier shoes.