As a nation state, Italy has emerged only in 1871. Until then the country was politically divided into a large number of independant cities, provinces and islands. The currently available evidences point out to a dominant Etruscan, Greek and Roman cultural influence on today's Italians.
If you are really considering it, you might want to look into "American Schools" in Italy. These are schools that teach in English and cater to Americans living temporarily in Italy who plan on returning to the US. These schools follow a traditional American program of study and allow the kids of American (and British) businessmen to move without missing a step in school. Here is a website with info on some of them. You have to be a EU citizen to work in most of them.
It's much less paperwork for anyone in Italy to hire an EU citizen. I have also been looking to teach English in Italy. The only realistic chance, in my opinion, for an American to work there is at a university. For any other school, it is really tough to get a good job without EU citizenship. I did get offered by a school in Rome, I pretty much would have been working illegally for peanuts, so I turned them down. Hopefully a lot of doors will open when I finally receive my Italian citizenship!
[In Teramo area] - Core / Fani / Venanzi / Secone / di Luca / Vannoni / Leteo / Bianchini / Cistola / Felicione / di Marco / Casalena / Romantini / Cintioli / di Francesco / Caponi / Foschi / Traini / d'Ascenzo / Ciare / Ciavattini
Don't let yourself be scared from the word "british" I believe that this isn't a strict requirement
There one of this private school in almost every town (say 100,000 inhabitants) so you can live in the countryside if you like or go to work by bike.
And I'm sure there are plenty of other schools that you can browse in the net. Even CEPU, which is an organization that helps students to finish high school and university possibly with good marks could be possibly interested into mother tongue english teacher.
Regarding the cost of life, if you can chose, pick up a town in central Italy: wonderful food, wonderful people, great weather, more than reasonable prices.