Thanks for the interest and for a great idea. I have a few suggestions that may help. with the third and fourth week.
First take a look at the type of climate you want to live in, Italy is mostly a mediterranean climate but parts of Italy are considered sub-arctic and some parts are very hot and very dry. ....
Second look at the type of topography you want to live in! Mountains, seashore, valley, it is all here. Tuscany is rolling hills but Italy has a lot more and many places that are a lot less expensive. Umbria, Abruzzo and Le Marche come to mind immediatly for the small village, that very homey feeling with fresh local food and a sense of community,. But much of |Italy has that in its small towns. That is why I stressed finding the topography and the climate you want first.
Finally for your last two weeks, I would rent a car and travel. and try to get lost. Italy has so much to offer that traveling might open your eyes to new things. Book BnBs or hotels on the fly and I have found that not using the standard BnB website can save you as much as 30% a night.
You are definately in for a lot of fun... enjoy and I hope this helps make your journey even more successful. Chip Stites, Italy Correspondent, International Living Magazine.