if meeting the locals is a priority then I suggest you look into a small family run b&b...though keep in mind, the major holidays are still pretty much celebrated and the owners maybe there - but they could also have quite a bit of family "stuff" going on. Or this is actually the last holiday before the vacation season starts so you might find that many have qualified stand-ins waiting to greet and register you. I would make a point of mentioning you desire to meet the family, etc. when you make the booking.
Here are a few family run bed and breakfast accommodations that you can look into:
Le Due Volpi
B&B del Giglio
PS. these links will take you direct to booking with the owner