Rent a car if you want to see some of the surroundings as well, because the distances in Milan are quite big. Taxis aren't cheap. A rental car gives you also the option to see Milanello, even though it's not open.
If you go by public transport, metro station San Siro Stadio is de westelijke endpoint of metro line 5 and is close to the stadium. After one of the matches you take one of the many trams behind the Curva Sud, back to the city centre.