I studied abroad in Naples, Italy with CIEE during Fall 2011. They say that the further south you go in the peninsula, the more "Italian" it gets, and you certainly can't get much more Italian than Napoli. I found the city absolutely fascinating and really enjoyed the full immersion experience that this bustling city had to offer. The city was founded by the Greeks in the 9th century BC, and that original historic center is still lived in, with apartment buildings built over Greek foundations and University buildings boasting Roman ruins in some of their lecture halls. I lived in an apartment with another American and an Italian university student in the neighborhood of Montesanto, right above the city's vibrant market area, packed with produce and seafood vendors, bread shops, macellerie, and a host of caffe bars. It was not an uncommon event to wake up in the morning to the sound of an accordian player in the alley below me, or to be stirred in the night by an impromptu firework show being let off in the neighborhood piazza. I very much felt that I was living the vita italiana!
I took classes in both English and Italian, and was able to also directly enroll in courses at the Universita di Napoli "L'Orientale." Not only was I the only American in my course, but probably the only one enrolled in a class at the University that semester. I found that living in the city helped improve my Italian immensely - very few in Naples speak English, and it is in fact one of the few cities in Italy where the local dialect is still very strong and frequently spoken, adding another layer to the city's cultural vibrancy (and also the initial language gap!). Some of my favorite memories include road tripping to the Amalfi Coast with my Italian roommates, taking frequent day trips to the islands of Procida and Capri (only 30 minutes by boat!), eating the world-famous pizza at Sorbillo, and of course the ritual night-time passeggiata when the entire city descends upon the streets of the centro storico and the lungomare to socialize, stroll, and grab some of Napoli's signature pastries.
I would absolutely recommend the city to anyone looking to immerse themselves in Italian language and culture, and who doesn't mind the hustle and bustle of a crowded, busy city. I've found that Italians tend to be incredibly accommodating and will often try to speak English with you (no matter how much they know!), and so my advice to anyone that wants to fully immerse themselves with the language is to definitely find a city well of the beaten track of tourism in the peninsula.
Follow this link for photos from my experience: http://www.flickr.com/photos/36679267@N07/sets/72157629353212274/