You could try the Orange Holiday SIM 3GB (about $25 on Amazon) which you can buy ahead of time and activate before you land in Switzerland. It's French SIM I think and is good for two weeks without registration. (Don't try to use until you are ready or you will start the two week period!) It is supposed to work in Switzerland and Italy. You can supposedly extend it past two weeks online, but it might be cheaper to use it for two weeks, then buy another SIM card in Italy for a four week plan, since you will need five weeks anyway. It looks like the 3GB plan actually gives you 8GB of data now - that's more than enough for the average person for two weeks unless you are streaming videos which eats up data quickly.
Don't be afraid to use Vodafone instead of TIM if one is easier to find than the other in Italy - I've used both there. You will need a passport in Italy to register a SIM, FYI, so take it with you to the mobile store when buying your SIM.
If you need to call home to the US, sign up for Google Voice now before you leave - the Google Voice app lets you call US numbers for free (even landlines) though you need mobile data or WiFi to make that work. You can text with the Google Voice app too - Google gives you another US phone number to use for that. (I use Google Voice for my regular calling at home in the US and get incoming calls too even in Europe, but that may not work for you, expect to be able to call out only and text.) While you may not feel like you need to call anyone while in Europe, it's nice to know you can call your bank or airline and be in hold for half an hour without worrying about chewing up minutes in a SIM card. (But would use data if you aren't on WiFi) And you can give people your Google number as a contact number - they can leave you a voicemail or text you at least at no extra cost to them.
If you will ever need to contact anyone in Europe while there, sign up for WhatsApp which is very popular there and free to use - again using mobile data or WIFi.