Which town for a base in Tuscany?

I adored Barga, up in the mountains. You can reach it by bus or train (I think bus might be better).
Pistoia sounds lovely.
I like the sea, so I would check out Livorno, Viareggio. Yes they are different and not the "Tuscan ideal," but if you like seafood they should be worth a trip.
We combined a trip to Lucca and Barga with a stop at the coast in Lerici. That area is really nice but more difficult without a car (we did it, but we were young and stupid and walked/grabbed rides everywhere back then).

Lucca would make a great base if you had a car, but if you're dependant on public transportation, Pisa would be easier since there are more direct routes to get somewhere than Lucca. Otherwise, you'll be needing to make connections which isn't fun.

Hi, I spent four days in Lucca, and I think there would be enough if you like activities, also. (But personally I like to move around more, so four days was plenty for me.). I took a cooking class from Extra Virgin there and recommend it. Also, you can take the train the short distance to Montecatini Terme which has some gorgeous historical spas and gardens with wonderful architecture.

If you can time your September trip to attend the Luminara di Santa Croce festival September 13th (check the date!) in Lucca, that would add to your experience.

The carrara marble tours might be a stretch to coordinate, but they are in the area, too.

Lucca is very flat, and the circular historical wall is very wide for a nice social walk, bike ride, or lingering on a bench. There was a local garden plant sale on a section when I was there.

We enjoyed Lucca, but didn't spend a week. I don't think I would want to spend a week in Pisa. We stayed five nights in Arezzo and four nights in Pistoia in 2017 and preferred Arezzo. You might take a look at it and see what you think. (We did all this travel on public transportation.)

If you’re open to switching to Arezzo as Janet suggested, their Jousting Festival, the Giostra del Saracino, is the first Sunday of September. I recommend purchasing the seats up in the bleachers ahead of time; the standing crowd gets wild with enthusiasm & rivalry. They also have an antique fair the first Sunday of the month.

If you were in Montepulciano, you know about the hilly streets. The medieval portion of Arezzo is also hilly. I stayed at a B&B in that area of town.

We stayed a week in Arezzo at an argriturismo. A week was too long but it's a good base because of the train station. We did have one of our most memorable meals there sadly, I don't remember the name of restaurant. Everyone was quite friendly. At the grocery store I had lots of help being taught the local shopping customs. It was one of those moments when I wished I could really speak Italian.

Since you've been to Tuscany a couple of times, have you ever considered visiting the Puglia and Basilicata regions? We spent a week going down the Adriatic coast and Matera a couple of years ago. So beautiful! It's just as beautiful as the Amalfi coast, but much more accessible. Matera is just amazing!! Nothing like it in Tuscany. Alberobello and the surrounding areas dotted with Trulli are just a whole other part of Italy worth exploring. Great food & wine. Just a thought. You can fly into Bari and rent a car.

From Lucca:
Lucca
NORTH:
Lucca-Aulla Scenic Railroad (through the Garfagnana valley)
Barga
Coreglia Antelminelli
Ghivizzano
Castiglione di Garfagnana
Castelnuovo di Garfagnana
Bagni di Lucca
EAST:
Pescia
Montecarlo
Collodi,
Buggiano
Montecatini
Serravalle Pistoiese
Pistoia

Thanks everyone for the great suggestions. Sounds like we can find plenty of things do see near Lucca. I also like the suggestion of spending time in Puglia. We plan to start our trip in Sorrento so Puglia might be a good option.

I've spent two holidays in Lucca, one of four nights...not enough; and one of two weeks...still not enough!
Lots to do and see in the town itself, it's slow-paced and has lots of places to sit and watch the world go by.
You can get buses from there to a few nearby towns and villages; or you can take day trips by train.
I was there two years ago in September, and it happened to be when the Luminaria di Santa Croce parade and celebration was on.
It was wonderful.
We watched workmen around the whole town spend the day attaching candles in holders to the walls of buildings on the parade route.
At dusk, every single street light was extinguished, and the candlelit parade began as darkness fell.
It took hours to pass by, and every service and religious organization was represented, including lots of visiting ones from other countries.
All very seriously done, but well worth experiencing!
We loved Lucca.

I love Lucca, have been twice. Surprised no one has mention Volterra. That has turned out to be one of my all time favorite places. I believe you can get there via train and bus from Lucca.