Which hill town would you choose?

A number of hill towns are accessible by taking a train to the base and then a local bus up. Perugia even has a little airport-like automated shuttle that takes you to the top. A nice guide to getting around the area is http://penelope.uchicago.edu/Thayer/E/Gazetteer/Places/Europe/Italy/Umbria/_General/accessibility.html

If by bus you mean inter-city bus I'd do that with caution. These buses are not meant for the tourist (although of course you are welcome to ride). Meaning their schedule is organized around the needs of people getting to work or school. They may run irregular hours and not much at all during mid-day, have many exceptions for holidays, nor for the most part should you expect to find staffed stations in most towns or drivers that speak english. Riding these can be a real adventure! Although perhaps that is what you want.

I've used Italian buses a lot for day-trips. It's true that there can be frustrating gaps in the schedule, but the scheduled buses have always shown up for me. The tourist office, which usually has an English speaker, can often provide bus information, though I always check at the bus station, too.

The footnotes on the schedule are important; don't assume that all the buses run every day. Seek local assistance if you hope to take a bus listed as not running on holidays, school days, or non-school days. Ask, "Is Tuesday a holiday?" rather than assuming they'll remember to mention an upcoming holiday.

It's quite likely that the driver won't speak English, so if you aren't really confident about pronouncing the name of your destinstion, write it down in block letters if it isn't shown on a ticket you've already bought. Most drivers are good about remembering which stops tourists need and will help you get off at the right place. Often other riders pitch in.

Except for Sundays, most towns of tourist interest can be reached by bus from the nearest city in the same region. Crossing into the neighboring region often requires a transfer. The real challenge lies in trying to visit two or more small towns in a day. Two can often be accomplished; awards should be given for hitting three little towns on the same day. If you manage that, odds are that you've skipped a meal. Or two.

With 3 nights in Florence and 2 in Siena, you barely have time to see those places. You may want to consider shaving one night off of Siena and take a train from Florence to either Assisi or Orvieto. Or, just stay in Florence. Then, day trip to Siena by bus. Then, train to Assisi or Orvieto for an overnight. You can train easily from Florence. Siena requires a Sena (Cena?) bus to Assisi with a change in both Perugia and Assisi. It takes time. There are limited bus time slots. Riding the train from Florence is easier. The bus between Florence and Siena is easy.
I want to add that if you have 2 nights in Siena - you can day trip by bus to San Gimignano. Just ask the hotel desk clerk in Siena for an afternoon wine trip in San Gimignano.

I assume you are taking one your days in Siena to do this?
you rent a car you could see more than 1 town as well as surrounding countryside which in some cases can be more of a draw than the towns themselves
From Siena you could do montalcino, pienza and montepulciano by car in 1 day
Or go less scenic in terms of country roads but larger and more famous towns by combing San Gimigingano and Volterra

Problem with public transit to any of these towns is the limited schedule likely will only make it work for one town to be visited in that day
There are buses to and from Siena to each of these towns.

I would recommend a car. You have freedom and much more latitude on what you will see. There is very little hassle to renting and driving in Italy, it is just like the US for the most part.

Many towns, such as Pienza, is best reached by car.. Other towns cannot be reached by pbulic transport. Multiple places can be visited in a day. For example, from Lucca we say Siena, Vinci, Monteriggioni, and all the scenery inbetween. on another day we went from San Gemini, Umbria to Orvieto, Todi, and Bormarzo.

My point is a car gives you lots, and lots, of options. Also, changing public transportation methods and enduring waiting times due to schedules, greatly reduces the time available to you to see things.l

The bus connections work well for seeing one town, I.e . Montepulciano from Siena. You might want to check our local tours which usually have a minivan and let you see a few towns and possibly a wine tour.

The bus connections work well for seeing one town, I.e . Montepulciano from Siena. You might want to check our local tours which usually have a minivan and let you see a few towns and possibly a wine tour.

I have found good information for traveling independently around Tuscany on the website 'discovertuscany.com' and they do have some information specifically on day trips from Siena without a car. https://www.discovertuscany.com/siena/what-to-do/day-trips-from-siena.html. It should at least give you some good ideas on how to get to these places by public transportation.

We loved Orvieto!!!!

You don't have time for another site. You have two full days in Florence which is not enough to even scratch the deep art heritage here. Two nights is one full day for Siena; Siena is a perfect one day town. Climb the Torre Mangia,

Visit the town hall and its art and its wonderful medieval mural of good and bad government; visit the church of St. Katherine and have lunch on the Campo. Stroll through a couple of close in Contrada seeking out their totem fountain and symbols worked into buildings and signs. And spend a good deal of time in the Cathedral one of the most stunning sights in Europe.

You don't have another full day which is what it takes to visit a hill town by bus.

Loved Orvieto (and especially Antica Olivaia with the hosts Daniela and Marco. Can't wait to go back there.