Help deciding where to go in June

During the first 3 weeks of June. I'd like to go to Italy as I've never been. I dislike tourist crowds -- yeah, I know everybody says that, but I mean it. Put it this way: If I could avoid it, I don't even care to go to Rome (but I likely have to fly into Rome). I'm not interested. (The only exception is Florence, which I wouldn't mind spending a day or two in solely for the art)

I'm looking for a place that isn't overrun by tourists, has some history & beautiful scenery, and perhaps has some transportation options in case I want to take day trips to other interesting places

Thank you!