Nothing to worry about!
Being our first time to Milan, well Italy in general; travelling always comes with first time nerves and this wasn't helped by many people including a man on the plane on our arrival to Malpensa, telling us to mind our bags because the centre of Milan is the 'den of thieves'. With this in mind we were apprehensive, but there was no need. Obviously theres a need for caution in any big city and watch your possessions, but Milan really is a lovely place and the Duomo is stunning!
Insider Tip:V. expensive try and find out online cheaper restaurants/cafes etc beforehand. also do make sure if you want to go inside the Duomo, shoulders covered and bottom half needs to be below the knee :D