marguerite,
To begin with, I assume you're aware that each driver listed on the rental form will require the compulsory International Driver's Permit for driving in Italy (these are also compulsory in Greece). These are used in conjunction with your home D.L. and are valid for one year. You'll also have to be very careful to avoid the ZTL (limited traffic) areas that are prevalent in many Italian towns, as EACH pass through one will result in hefty fines which you may not know about until several months after you return home.
Regarding the SIM card, you can certainly use your phone for GPS. AS the previous reply mentioned, TIM and Vodaphone have "tourist packages" which are quite reasonably priced. It may take a few minutes to set the phone up with an Italian SIM, and be sure to bring your Passport as it will probably need to be registered. While the GPS system isn't dependent on cellular access, you'll need data to download the maps. It is possible to download offline maps, but I find it easier just to use cellular data.
Another option would be to use international roaming with your home cell network, which may not be that expensive. Finally, you could also buy a dedicated Garmin or TomTom GPS unit equipped with European maps, and that won't require any cell data.