Tuscany and Umbria have incredible hill towns that most tourists skip because they're harder to reach, but that's exactly where you'll find the real Italy away from selfie crowds. Same goes for trattorias in small villages, the food there beats anything in Florence or Rome city centers. To actually get to those places you need your own transport though. You can rent a car in Italy here
https://getrentacar.com/en-US/italy . Listings from local owners across different cities, you can filter by car type and price range, read reviews from previous renters, and book directly with the owner who'll meet you at a convenient spot.