Lucca or San Gim

The "easier" of the two to reach by public transportation is Lucca, as there are direct trains from Florence about hourly. You can also go by direct bus, which can be a bit faster if not traveling at rush hour. To reach San Gimignano, one must take a bus or train to Poggibonsi and then change to another bus to San Gimignano. The change isn't difficult, it's just not direct.

No comparison . Lucca is far more interesting and complex and (relatively) much less crowded with tourists.

Thanks very much for info, Lucca was my choice, now I just have to convince my friends that I’m traveling with.

I stayed in both towns, and while very different, I found them both enjoyable. Lucca is flat, with a wide wall surrounding the town, so wide that there is really a park on top, and you can go up steps at various points and can walk or ride a bike around the town, picnic or play up there. Also some ancient buildings, a tower to go up, and several old churches, good restaurants, plenty of shops, plus a beautiful Grom gelateria in an old building, at least when I was there in 2013. There are various forms of Puccini musical performances virtually every night if the year, vocals or instrumentals, as Lucca was Puccini’s birthplace. I found Lucca to be a very livable town.
San Gimignano is a stone hill town, certainly more hilly, and more of a tourist town. When I was there, I sent an e-mail to some friends back in the US, and they responded — “ah, the Manhattan of Tuscany!”, referring to the many towers rising from homes in S.G. In the day there were 75 towers, now reduced to 4. From the main entry gate into town, there is an uphill street which is very touristy and commercial, with many shops, delis, restaurant serving visitors and one or more viewpoints overlooking the Tuscan countryside. When you reach the main piazza, with a fountain or well I. The middle, there are two excellent competing, almost dueling, gelaterias, one aggressively selling itself as the national champion of a few years earlier, the other simply with a sign which read “ best in the world”, at least back in 2013. Since I was in town for a couple of days, I found both were delicious and fun. Once you wander past the main square the town is extensive and much quieter, with very few visitors, and there is another fine church, a wine museum with tastings, and great views for photography.
So, clearly, extend your trip for a while, and spend a night or two in each of Lucca and Sam Gimignano!

Visited Lucca on Friday. Lovely town, compared to Florence it was a nice day trip to get away from the crowded city. Enjoyed strolling the city wall and seeing the town. It was an easy train ride from Florence and it was recommended to me by people on this forum. So glad we went. Next time I’d like to spend a couple of days there.

There's a typo in Larry's posting. 14 towers survive in Sam Gim, not 4.

Lucca, hands down.

SG while interesting in its own right, has attracted and fallen prey to over-tourism. I found it overrun with day-trippers and a little too many shops focused on cheap currios.

Lucca on the other hand, while it has its tourism traps, I found to be much more interesting. The old town is set inside the fortified walls, the streets are a narrow maze similar to Venice; a piazza or, neighborhood church clearing poping up here and there. There's a number of interesting shops and the restaurants serving their distinctive tortelli lucchese. The surrounding hillside has a large number of rentable villas also, makes for a nice home base as it sits geographically in-between Cinque Terre and Florence.

I cast another vote for Lucca. Direct train trip, easy to get to from Florence. Such a pretty town, easy to walk and the city walls are a park. San Gim is nice, but after a couple of hours there, I was done. I spent a whole day in Lucca and am already yearning to go back.

Lucca is a worth a day and San Gim about two hours.

I am sure you could train to Lucca, not sure about San Gim.

Without question, it's Lucca! Besides being a much more interesting place, it's a quick and easy train ride from Florence. You could also hop over to Pisa in a very short time by train. Seeing both places in one day trip is not at all hard to do. Trains leave early and return late and tickets are cheap, especially when purchased in advance. Pisa's leaning tower is overrated and totally overrun with long lines and selfie sticks, but the closeby cathedral is fabulous! You need to reserve an entry time.

You won't need a lot of time in Pisa compared to Lucca. You can read about San Gim and see photos on Google. You won't miss much IMO.