Extended stay in Tuscany

Florence (especially) and Siena seem to have by far the best public transportation options. For such a long stay, I would not want to be in a small town. I especially wouldn't choose a place without a train station I could walk to or reach by a frequent city bus. That means no hill towns with train stations 2 miles (or 10 miles) away.

Is it necessary to spend your entire time in one place? Tuscany is rather large, and you'll find it easier to see it if you have at least two bases.

If you are a US or Canadian citizen, you cannot stay in the Schengen Zone for more than 90 days within any 180-day period. Italy is in the Schengen Zone. Both the arrival day and the departure day count. Therefore, you cannot stay for 3 full months unless you obtain a long-stay visa. Overstaying the 90-day limit is likely to lead to a sizable fine and being banned from re-entry for a number of years.

Phil - I would recommend Lucca and Pisa as good bases. Arezzo is also another option. Why not choose 2 bases for the 3 months you will stay in Tuscany. One base can be in Chianti region and another base in Umbria region. For the 3 months, you can spend half in one region and half the other. That way, you will have the opportunity to visit and explore as many towns as you want.

Any provincial capital city in the region would have the best public transportation options for that province. So depending on the portion of Tuscany you want to visit, you may want to stay in the logistically best situated provincial capital.
The 10 Provincial Capital cities of Tuscany are:
FLORENCE (Provincial and Tuscany Regional Capital City)
SIENA
LUCCA
AREZZO
GROSSETO
PISA
LIVORNO
PISTOIA
PRATO
MASSA & CARRARA

I would choose the first 3 or possibly 4 (Arezzo) in the list as your bases
If the Maremma area (Southwest Tuscany) is in your plans, then you need to add Grosseto. Maremma is too far from any other location and a rental car is recommended because it’s the most rural part of Tuscany.