Milan is a beautiful city, full of beautiful and friendly people. There are also a lot of tourists here so it would be good to meet people from other parts of the world. I recommend to use the free walking tour service. It's tip-based so if you're happy with the tour guide, you can give him or her a tip after the tour. Tip ranges between 5 to 50 euros.
There are a lot of plaza squares in Italy which they call 'piazza.' This one in Milan is called Piazza San Fedele