Florence to Rome

Rural Tuscany is not well served by mass transit for tourists. Siena and Arezzo are larger cities served by train - best from Florence - and smaller towns like Cortona (by train + bus) are reachable but day tripping or changing towns is difficult.
Orvieto is another small town worth visiting - although it is technically Umbria - along the Rome - Florence line.

Here is a good image of what is accessible by train or train+bus: https://www.wanderingitaly.com/maps/images/tuscany-rail-map.png

If you want to take a couple of slow days in a town it is certainly possible to stop off along the way, but visiting a couple of towns in a couple of days starts to pose some challenges. Also note that the train between Rome and Florence is very fast. If you choose to stop in a small town the train will be much slower on both sides of that trip - probably taking twice as long. If you're spending a couple of days this isn't a big deal but if you plan on stopping for lunch somewhere along the way the trip will take much longer.

Hope you find your spot,
=Tod

Orvieto is probably your best choice without a car
Right on the train line
It is an Umbrian hilltown not Tuscany but close.
Has an amazing Duomo, great views, underground history/ activities, very good restaurants

Otherwise you really need a car to explore Tuscany hilltowns/countryside

As mentioned above, the trains from Florence to Rome are mostly FrecciaRossa high speed trains that cover the distance in 90 minutes and make no stops in between.

If you want to stop in between for a few days, the only option is to take the slower regional trains or buses. Either way those means of transportation would prolong the trip since they are not super fast like the Frecciarossa trains Florence-Rome.

Besides Orvieto (Umbria), Arezzo and Siena are both viable options in Tuscany.

For Arezzo you would take a regional train from Florence. There are many trains throughout the day, nearly all of them are Regionali Veloci (RV), or Fast Regional trains, and you can be there in 45 to 80 min (depending on which train you choose). Arezzo itself can be visited in one day (so 2 nights would be sufficient), but if you want to take day trips from Arezzo to Cortona or Anghiari or Castiglion Fiorentino (very famous hilltowns in the Arezzo province), then you need to stay more nights. There are also a couple of very fast Frecciarossa high speed trains from Florence to Arezzo, which would get you there in a little over half hour, but they are early in the morning (like 6 and 7:15).
From Arezzo to Rome there are several trains, mostly Regionali that take over two hours, but there is also a couple of FrecciaRossa high speed departing early in the morning.

For Siena you would take a bus from Florence (faster than the train).
Like for Arezzo you need a day to see Siena, so 2 nights are perfect.
For more day trips (by bus) to nearby towns (many in this province), you'd need more nights.
From Siena to Rome the fastest way is a bus to the Rome Tiburtina bus station. FlixBus and other companies cover that trip in about 2.5 hours.

I second the suggestion to go to Orvieto - lots to see, good restaurants, hill town. Years ago I listened to a converstion between Rick Steves and a local guide discussing the differences between Tuscany and Umbria. The upshot was there's basically no difference. That was also my experience for 9 days with a car - I couldn't tell whether I was in one or the other, except for small signs at the borderlines. Some days I went back and forth more than once.

Well, the Tuscan and Umbrian dialects are very different. Tuscany has its own pack of dialects, mainly recognized by many aspired "c"s, so "casa" that in standard Italian is pronounced "kasa", becomes "hasa" in Florence. There is a famous joke that a Coca Cola in Florence becomes a hoha hola - but not all the "c"s are aspired.

Umbrian dialects are close to Roman dialect. Even if the speakers are speaking standard Italian, they will often maintain their dialects' phonetics. So there is a very clear linguistic border. Of course, this is a detail mostly lost to non natives.