I am just really interested in the culture and want to stay not so
much in the cities but in rural peaceful areas.
Hi Cheri and welcome to the forum! Penpals? You've found oodles of them right here as the Italian forum is, along with France's, probably the most active of the RS European Q and A spaces.
"Culture" is sort of a nebulous term but you will find Italians living their various versions of Italian lifestyles anywhere that they live, including the cities. The cities - and you did mention interest in Rome, Florence and Siena - also tend to have concentrated areas that are especially rich in cultural/historic art and architecture. I would caution you not to try and stay outside of them and travel in every day as the historic centers, while busy, are where you're going to want to locate for most efficient and enjoyable sightseeing.
You didn't mention what time of year you're thinking about taking this trip? Keep in mind that "peaceful" is also a bit of a nebulous term and may be a challenge regarding most-visited locations during high and shoulder seasons. Staying in those places versus day-tripping them from outside is a good work-around; it allows for some golden hours before those day-trippers arrive and after they leave in the late afternoon.
You'll also want to consider how you intend to get around? Staying in the countryside often involves renting a car, and driving/parking in Italy comes with its own set of challenges. You certainly don't want a car for the cities or for the coast, depending on where along the coast you want to go. Some folks rent just for a few days to bop around rural Tuscany or Umbria but that doesn't mean they're allowed to drive right into every old, picturesque village so some homework is involved there.
A combo of guidebooks + info gleaned from the folks here will be a great start for your research. :O)