The Italian word ciao has crossed borders and is a popular greeting all over the world, so “why shouldn´t I use it in Italy?”, (even Rick Stevens is using it) you could argue. You´re right, ciao is heard all over Italy, but it´s used by Italians to their Italian friends or family members, not between strangers!
It´s not polite at all to greet someone you don´t know or someone more senior with ciao, the Italian society is very formal, even if it doesn´t look like it from the outside. Assuming you´re a tourist, travelling Italy, the perfect greeting to say hello would be Salve. I know it sounds like jumped out of Asterix and Obelix, but it works. Italians will recognize that you´re familiar with the customary practice and don´t treat you like a simple tourist. The only quirk with Salve is that you can´t use it for goodby, but this problem is easy to solve: Depending on the time of the day you can say buongiorno (good morning) or buona sera (good evening), this way you don´t get into trouble with formal or non formal greetings. There is another Italian word you can´t use: arrivederci (bye). It sounds beautiful, but it´s also informal, the formal version would be arrivederLa……do you want to get into the details?