Hi. Welcome in Italy! Wish you a great stay in our Capital City.

Mostly agree with Fausto here. Like in many other EU countries, the Laws about knifes carry in Italy are based on the justifiable reason principle. Under this principle, you are basically allowed to carry whatever is suitable for the task you have to carry out. The downside of this is this principle, as said, is very discretionary and based on subjective LEOs evaluation.
Italian Laws in a nutshell:
Daggers, flick-knives, double-edged knives and bayonets are considered weapons and one needs a gun permit for buying these and are never allowed outside own premises. Any other knives, in all possible different shapes or sizes, are considered cutting tools under the justifiable reason principle. Sale and possession are free if you are an adult, the carry is allowed exactly under the justifiable cause. So if you are working, hunting, camping, farming, gardening, involved in outdoor/sports activity, etc. you are allowed to carry whatever is suitable for the job. These becomes improper weapons as soon as the justifiable reason to carry is gone. Normally, according to Courts sentences, in
urban areas in Italy, this justifiable reason to carry is almost never there. Basically
urban EDC (i.e.: I carry just in case I need) is
not considered as a justified reason to carry a knife. Under the same principle, while its perfectly OK to go to own vegetable garden in rubber boots with a roncola hanging from the belt, the same attire can drive you to jail when in the financial district of Milano.
Also, still, in Italy we have a rather high level of alert (against terrorists attacks and for illegal immigration issues) and several cities and towns are patrolled by the Army as well, which have been given some police tasks and authority. So Id say its not recommended to wave Rambo style knives in the Colosseum or Piazza Navona. Carrying a SAK, a small Opinel or a traditional of sorts, its generally accepted when youre a tourist, if one bears, acts and behave in a respectful and appropriate way.
Now, as a personal reflection, setting aside all the critiques we might raise about the discretionary power, subjectivity, poor clarity, etc., the
practical effect of the justifiable reason to carry works very well, at least according to my experience. Along my many years of knives EDC, I never had a single issue with carrying a SAK or a small slip-joint as a tourist, in urban areas. I have peeled oranges, apples, peaches for wife and kids, cut my sandwiches, salami, etc. in many squares of our beautiful Italian towns and cities, with Polizia or Carabinieri just few meters away. On the other hand, I have seen several times too exuberant teenagers, people with exaggerated/improper behaviours, suspicious individuals questioned, searched and fined for the possession of a strange keychain, a blunt screwdriver or a box cutter. Which makes sense and its rather effective, at least in my opinion, in spite of all those claiming its just a shame, a Police State approach, etc.
Stay safe and enjoy your travel! Take care.