Home base in Tuscany region

You would do best staying in Florence unless you had a car.
With a car, I prefer to be outside Poggibonsi or San Gimignano in the countryside at an agriturusmo.

In all my years of traveling to Italy (30+), I don't know anyone who visited Tuscany and relied on public transportation. On the ground, it seems like a serious amount of work with a lot of time wasted. Many Tuscan resorts caution visitors against a visit without a car. And god forbid you're stuck in unpleasant weather. Planning is a challenge because every move must be calculated on a reliable timetable. If you screw up and miss a connection, you could easily find yourself stranded for twelve hours. If you don't know Italian, the challenge and frustration intensifies.

Florence is the capitol of Tuscany. I hear that tourists do frequent trips from Florence to various locations within Northern Tuscany, using public transportation. There is a lot to see and experience within an hour of Florence. Loads of information is available on the internet to help plan and organize this type of trip. A lot of reading and learning is required to do it successfully on your own.

Bologna is wonderful but not in Tuscany. Florence is much closer to villages and the countryside.

Consider renting a car. Driving is not a problem in Italy. Check AutoEurope for car rentals in Europe.

I have used the app rome2rio for getting to some out of the way places in rural Veneto.

It works pretty well, gives a variety of travel options like car, taxi, train, train+bus etc, and links to timetables for train and buses. That being said, the bus timetables can be a challenge to interpret, the rail timetables are more simple.

If you plug in your home base and destination, you can see what is doable.

I have traveled extensively in Tuscany without a car (and with a car when traveling with friends). Unless you want the agriturismo experience, you can visit many cities and smaller towns by public transportation, for example, Pisa, Lucca, Siena, Anghiari, Sansepolcro, Pienza, Arezzo - you get the picture - by basing in Firenze.

If you want to visit some other places, there are many daylong tours that will take you to two or three towns, a winery, and a lunch stop. And you don't have to worry about driving after a few glasses of vino.

If you base in a city such as Florence you do not need a car to see many of the wonderful places in Tuscany. If you want to base out of the city at an agriturismo then you will need a car. I think Florence is the best larger city to base in because of it's easy train connections to other towns and the availability of day tours that will get you to those hill towns with less than perfect train connections. As has been stated on here before, buses are not the most efficient for day trips to smaller towns as their schedules are not always frequent and flexible enough to suit tourists. If you want to stay in a smaller town then I would recommend Montecatini Terme as a good base. Good selection of hotels, restaurants, etc. and good train connections with larger towns like Florence, Siena, Pisa, and Lucca.