If you are traveling with a car lover, Ferrari has their factory in mid-Italy - museum, tour, and you can hang over the fence and listen to them test drive. Also see some test products out driving in the area sometimes.

A restaurant in Siena is making pasta by hand and you can watch the process as you eat.

Italy has a number of Italian language schools in various cities around the country. Roughly 1/2 time so one can do quite a bit of touristing on weekends and some afternoons. Not terribly expensive and you learn a lot.

I spent 6 days in Venice once, just deciding on the perfect chandeliers for my house. (Actually made the decision at the 5th day so took a train ride to the home of Palladian architecture and wandered there for a while). Murano and Burano each worth a nice chunk of time, and just riding the No. 1 boat around the Grand Canal, both day time and night time as the effects are quite different.

The Isle of Capri is heart-break beautiful.

If you go to Pompeii, you also need to go into Naples to the museum where all the small artifacts were taken (to protect them from weather and probably also to keep them from walking off). Herculeum is similar to Pompeii but not quite as developed. Worth a look also.

A week would probably just barely let you do a good job with Rome.

Pull an armload of guide books from your local library and take a note for everything that really grabs you. You'll decide that 4 weeks isn't enough.

A ferry to one or more of the islands?

Keep a list of each flavor of gelato you've tried.

And now you've got me wanting to go back - Romelle