What time of year? Some slightly off-the-beaten-track suggestions:
1. In August in Tuscany, all of the little hill towns have festivals celebrating some local food, like duck, ravioli, truffles, etc. For these you need a car, but they are really small and local (except the truffle one, which was comparatively huge) and fun. There is, of course, no website or general listing of these things, because that would require too much organization and structure. :-) We found out from the guy we rented a house from.
2. In Tuscany, Arezzo is a cheaper place to stay than most of the other, more well-known destinations, and still very cool and with direct train access/adjacent to the A1. There are also great small winemakers in the area -- the kind you discover after a few miles down a dirt road -- that are more inexpensive than the more famous ones across the highway (happy to provide names, feel free to PM me).
3. Florence and Chianti are massively expensive; good for day-trips.
4. I loved Montepulciano for the geography and the views -- truly a spectacular town. Park at the bottom, take the bus up for 1-2e, and walk down. Many, many places to taste wine, and the Rosso is cheap and good (the Vino Nobile is delicious but more expensive, although it is still a deal compared to its big-brother Brunello from Montalcino, the next town over). Many many tourists, but worth it.
5. In the lake district, Como is the most famous, and so also most expensive. The lake the Italians all vacation at is Maggiore, and prices are a little more reasonable (though still very high by comparison).
6. Between Tuscany and the lake district you can swing through the Piedmont, home of the best wine ever made IMO (Barolo). But it is also the home of some of the cheapest delicious wine ever made, Moscato d'Asti. Again, there are many small winemakers in the various small towns and hills.
7. We stayed a few nights in the small towns in Emilia-Romagna where prosciutto di Parma comes from (the Langhirano) -- smaller, less touristy, very nice people. If you want specific recommendations, feel free to PM me -- we stayed at a great B&B up the hill with a family with two boys who were about my son's age, and they couldn't have been nicer; they set us up with prosciutto and parmigiano tours.
8. The splurge that is worth it: aceto tradzionale -- the famous stuff is from Modena, of course, but I got a bottle from Reggio Emilia that I actually prefer. This is where you want to drop $100+ on a 25-yr-old bottle, which is more like dessert than vinegar. I still have half of the bottle I bought in 2013; in fact, I just had it for lunch the other day drizzled over peaches and ricotta. Again, PM me for more details.
9. Try the ricotta -- like nothing you get here, I had it for breakfast every day on bread with jam -- and the porchetta. Oh: in Rome, go to the Jewish quarter, and get Carciofi all Giudea (artichokes in the style of the Jews). They are fried in olive oil and so ridiculously flavorful and delicious you will not believe it. I bought a Molto Mario cookbook specifically for this recipe, and I still can't make it taste as good! I am serious about this. I'm not even a huge artichoke fan, and I am haunted by those things. And the porchetta. :-)
10. Wherever you eat, just get a carafe of the local red -- it's always delicious, and very cheap. BTW, did you know you can bring wine home as checked luggage? They sell boxes with styrofoam inserts that can hold 12 bottles; we put our clothes in carry-ons and brought two boxes over empty as our checked bag, so we could bring them back full. :-) You do have to declare it at customs, but the duty is so low that most of the time they just wave us through and don't even bother to collect. And if you like any of the wines, it's sort of ridiculous how much cheaper they are over there than if you try to buy them here.
11. The trains are great between the big towns, but a lot of the fun stuff is in the hills, so consider renting a car for parts of the trip to see the less-touristy areas. None of my favorite spots were on a reasonable train line. Driving is really NOT bad outside of the big cities. (And honestly, my DH was totally comfortable driving in Rome, but then again, he learned to drive in Jersey, so YMMV).
12. Try AirBnB and HomeAway and Fewo-Toskana for places to stay -- you can frequently find better options than staying in hotels. Plus many of the towns have a weekly market, and so you want a kitchen to be able to come home and cook up the deliciousness that you'll want to buy. :-)
13. Every area, every town has its own food and wine specialty, and they are convinced that they do it "correctly" and everyone else is wrong. :-) The Piedmont, for ex., is known for agnolotti; the area of Tuscany where we stayed is known for wild boar (cinghiale) and the "white pig" (cinta senese); other towns are known for specific cheeses; some of the mountain areas offer fricco (like a parmesan crisp but made with montasio and not quite as crispy but ineffably delicious); etc. Whatever you do, get that specialty.