The main mobile phone carriers in Italy are: Tim, Vodafone, Wind and 3 (Tre) and PosteMobile. They all have shops close to Bocconi and all offer both contract and pay-as-you-go cards.
Generally, Tim and Vodafone are considered to be the best in terms of coverage and network reliability (which is an issue sometimes, especially outside of the urban areas). Wind and 3 are the cheaper alternatives.
Pay-as-you-go is available for everyone and may be a good short-term solution upon arrival in Italy. Contracts, most of the time, require an Italian bank account number. It is however possible at some shops to give your credit card number.
The shops will ask you for your codisce fiscale. A way around this would be to auto-generate it online before getting your actual one. Normally Bocconi requires you to do so during the admissions & registration process anyway. In any case, you can generate it again online.
Switching between carriers is usually easy (do verify beforehand) and normally you will get to keep your number too.
Below, you will find the phone shops closest to Bocconi:
Viale Bligny 2
Tel: +39 02 36593183
Opening hours: Monday-Friday, 10:00am-7:00pm
Corso San Gottardo 5
Tel: +39 02 58108154
Opening hours: Monday-Saturday, 9:30am-7:30pm; Sunday, 11:00am-7:30pm
Viale Bligny 16
Tel: +39 02 39469324
Opening hours: Monday-Saturday, 9:00am-12:00pm, 3:00pm-7pm
Viale Bligny 26
Tel. +39 02 58432044
Opening hours: Monday-Saturday, 9:30am-7:30pm