Small towns to visit near Florence?

Pisa and Lucca (double »c«) are easily done on a combined day trip. Use the website of the Italian railways for schedule and prices.
When in Pisa, don't forget to visit the cathedral and baptistery in the same complex. While the tower is emblematic, you'll probably find the baptistery the most impressive.
Another worthwhile and easy day trip is Siena, and probaby nicer than San Gimignano for the young one. Best done by the bus which leaves from the bus station across the square from the railway station.
It's all straightforward, so you can easily be master of your own time and taste instead of getting on some tour.

If you have just one day for a day trip then Siena gets my vote.
Wonderful hill town easily connected by bus to Florence. Note that the bus leaves u right in the old town whereas the train station is at the bottom of the hill.
It has one of the best squares in Italy the piazza del Campo and the view from the bell tower is spectacular. The cathedral is superb and the medieval hill town atmosphere is great.
In Pisa if you have to see the tower, make sure that u see the cathedral, baptistery and the Camposanto cemetery , they deserve more time. Lucca is a wonderful little walled town with fewer tourists but not as spectacular as Siena.
San Gimignano is too touristy .if you had a few more days then maybe you could have given it a shot. With just 3 days, Florence itself will hardly give you any time to move around a lot.

Hope that helps you decide.
Have a great trip!

Forgot: the Italian railway tool doesn't know a city called »Florence«. In Italian it's »Firenze«.

In the corner of the pisa complex near the bapistry is a museum that shows a video cartoon of attempts thru the centuries to straighten up the tower.... very school house rock but fascinating. You probably arent allowed to take a toddler up in the tower.... the website will tell you as you look up timed tours. Bapistry or cathedral will be a better choice

Honestly, if you have only 3 days in Florence I would say to stay there. There's so much to see! And the wines from the surrounding regions, especially Chianti, are readily available in bars and restaurants in Florence.

Or if you really want to get out of the city for a day (or part of a day), go to the "suburb" of Fiesole. See, for example, https://www.visitflorence.com/fiesole/

While you could easily spend all 3 days just in Florence, I'd suggest Lucca with a stop in Pistoia if you decide to do a side trip outside of Florence. Both towns fit your criteria and are relatively flat should you have a stroller. Pistoia is on the Florence-Lucca train line, 35 minutes from Florence and 45 minutes from Lucca. Wineries generally aren't easily accessed by public transit, so a tour might work best.

Traveling with a baby will make everything more of a challenge and take much longer. I agree with the people who say stay in Florence, but probably the little one won’t want to spend half a day in the Uffizi. Keep your itinerary loose and casual, and find outdoor spaces to visit, like Piazza Michaelangelo. If you really need to go somewhere else, Siena, a fantastic medieval hill town with an incredible Basilica, great restaurants and a fun nightlife, is my choice for a day trip, although I’d your next stop is Rome, I would spend the night in Siena. As others have said, the bus is the best way to get there.

This tour will give you a taste of the Tuscan countryside. Two towns in the Chianti region, Greve & Castellina and two wineries. What I don't know is if it would be too long for your child.
A stroller would be advantageous.

https://www.getyourguide.com/florence-l32/chianti-wine-tasting-half-day-tour-from-florence-t4433/

What about renting a car with a baby?

You can visit Montecatini and Montecatini Alto by taking a short train ride from Firenze (SMN) and back. Might be a good little trip for you guys. Florence is all consuming so you might not make it out of town. Is it actually three full days or are you eating some of that traveling elsewhere. Three nights = two full days.

With such short time I would get a tour guide. I highly recommend http://www.alessandrocammilli.com/.