Hello Mike, I cannot help you with schools in Italy, since Italian is my native language. But I can share with you my experience about "full immersion" in other languages. It surely is a good experience to go to a medium size city with cultural activities and were people are not too much stressed. I used to visit museums with local audio guides, go to theater, and to the movies, sit in cafés and listen.Besides collective courses I would definitely also take every day a private conversation lesson.
if I would have time and money I would choose a program which offers homestay at a teachers house.
For Italian I think Torino would be more relaxed then Milano.
Buon viaggio!