I have a "safety strap" for my camera which has a steel cable molded into the strap. It is impervious to "slash and run" attacks and is a pretty darn comfortable strap.
http://www.amazon.com/Pacsafe-Carrys.../dp/B00HSJNFKS
Another piece of advice (which is generally applicable to any travel photography) is travel as lightly equipped as possible and at all times be cognizant of your equipment and your surroundings. It is always best for two people to be together, especially if one is shooting and the other is not. That way, the non-shooter can keep watch for the shooter.
Never venture into any area in which you get bad vibes for safety. Additionally, be careful of any local who becomes too friendly and wishes to guide you to a "spectacular place to photograph". Do a Google search with the search parameters of "Safety in Rome".
When I am traveling, I don't carry a wallet. I wear a holder somewhat like this one
http://www.amazon.com/Pacsafe-Carrys.../dp/B00HSJNFKS around my neck and under my shirt or jacket. I keep passport, credit card and other ID as well as my main cash for the day in bigger bills. I always make sure that I have smaller coins or bills which I carry in the front pocket of my trousers. When I need to replenish that ready-money from the bigger bills in the wallet, I do so in a secluded or private area such as a restroom. That way, I never flash a large quantity of money.
However, with some safety precautions, you can have a wonderful time in Rome (or any other large city). I usually try to wander into the residential sections and get photos of people going about their daily life, shopping, working, etc. like this morning rush hour in a Chinese alley.
I have visited many cities in both Europe and Asia with no problems and, I WILL BE 75 IN JUNE!