The Island of Elbais the busiest and most popular of the Tuscan archipelago, but on the other end of the spectrum, visit the tiny island of Giannutri for a moreoff-the-beaten-track experience. Just 5 km long, it has a year-round population of 20, but sees more activity in the summertime when the daily 90-minute ferry starts from Porto Santo Stefano.
It is easy to incorporate a day of diving into an Italian tourist itinerary. For example, Monday: explore Tuscan hill towns; Tuesday: diving; Wednesday: visit a museum and do some wine-tasting. And Giannutri is a great day trip: catch the 10 am ferry, and return with the 4.45 pm one; you're back at your hotel with time to freshen up before dinner.
If you want to stay overnighton Giannutri, it's possible, but there is no hotel on the island and camping is not allowed. Call the island's restaurant, La Taverna del Granduca, and they will set you up with accommodation.
If you need gear or a guide, contact Scuba's Angels, based out of Torino, and they will make sure you are organized.