First, I would say that you're already providing them with a tremendous service in giving them a place to stay, so I would take some of the pressure off yourself. Obviously, they're coming for the locale, if they haven't visited for years before you moved to Italy.
Second, there are guide books and website to find activities, and they will probably have things they want to do. So, approach as an opportunity to explore your new city together. Try out new restaurants, do some sight-seeing, let them pick activities; not everything has to be pre-vetted. Heck, I love going to markets to shop for food in new places. Maybe they'll enjoy that. Everything is exciting when you're in a new place.
As far as hosting, I'd make sure to have a comfortable spot for them to sleep and some food in the apartment for mornings and snacks. I would not feel pressured to cook every night, and they can certainly help out since you're already providing some food and a place to stay.
As an introvert, you also need to take alone time when you need it. You haven't seen these people in years, so you may feel an obligation to be with them every moment and always have something planned. Resist this temptation. You will be burnt out and potentially quite unhappy by the end of the trip, which has the potential to damage your relationship if you start snapping at them (maybe that's just me?). So, build in alone time. Give them time to read books while it's raining. You aren't a tour guide. You're a friend who happens to live a fun place.