Florence Day Trip??

Just returned from Italy, spending 12 of the days in Firenze. I did a 2 day trip to Assisi. However, I ended up returning to my Firenze room after one night in Assisi. I also visited Chiusi and an agriturismo between Certaldo and San Gimignano. Although they are both picturesque, I like Certaldo better. Less touristy. I would also put Greve on your maybe list. Try to research a place that is off the beaten path a bit.
I also have some suggestion in Firenze if you are interested.

If I had to choose just one it would probably be San G. Yes, it is more touristy, but the tourists go for a reason. It is beautiful and there are far more options for food and shopping there than in Certaldo Alto. I did love Certaldo as well, but I photographed an intimate wedding that was held in the church there... so I have some nice memories, but I do remember out dinner choices were rather limited. But, I think any Italian town you choose to visit can be enjoyable... after all, it's Italy.

One of my most memorable travel days, even though it happened in 1989, was going from Florence to Lucca in the morning, then to Pisa in the afternoon, then back to Florence. Bicycling on top of the wall around Lucca was great. By the time I reached Pisa, the souvenir vendors were literally packing up, and the marble buildings on the Field of Miracles looked lovely in the afternoon light.

If you like wine, tour some vineyards and wineries in Tuscany.

Day trip. Train to Monetcatinni Terme, up to Montecatinni Alto, then on to Lucca, have dinner, then return.

We had a great experience with Accidental Tourist. Van picked us up (8 people total who split into 2 groups) in Florence central meeting spot, drove out to vineyards/winery for tour and tasting of several wines and olive oil, then on to a pasta making lesson at a house where our Italian hostess was lovely and served a delicious lunch that included among other things our pasta, quiche made with freshly picked chard, and finished with espresso and the best tiramisu any of us had eaten (apparently just-laid eggs and using all mascarpone makes a big difference. I swear it was so light it practically floated. Anyway, I digress.). Our guide was a friendly opera singer who treated us to arias as we rolled our fettuccine. The lunch setting outside under a tree looking across a valley to a castle was picture perfect. Not having to worry about transport was very relaxing.

We did exactly what Harold did, in 2008. Lucca is Puccini Central, if that matters. We rented a tandem bike, had a lovely lunch and moved on to Pisa. A very nice day and easily done with short travel segments.

We had a 'free' day in Florence and took the recommendation of a friend and visited Verrazzano Castle and Winey in Greve in Chianti. http://www.verrazzano.com/en/the-castle/ It was one of the highlights of our 2 weeks in Italy. We reserved our tour/lunch/tasting ahead of time and we followed the directions on their website for taking the public bus from Florence. I can speak some basic Italian so I just asked the bus driver to tell us when to get off and where to catch the return bus. It's about an hour ride through towns, but it's scenic. It's quite a climb up a hilly driveway to the castle/winery but beautiful views. If mobility is an issue, stop in their wine store at the bus stop and perhaps someone can drive you up. We found that out after we got up there!
We left Florence at abt 8:45 am for an 11am tour and we were plenty early, but we wanted to allow buffer time for getting lost. This was living as the locals, riding with the locals.....aka through the back door. Great Day!

We had a 'free' day in Florence and took the recommendation of a friend and visited Verrazzano Castle and Winey in Greve in Chianti. http://www.verrazzano.com/en/the-castle/ It was one of the highlights of our 2 weeks in Italy. We reserved our tour/lunch/tasting ahead of time and we followed the directions on their website for taking the public bus from Florence. I can speak some basic Italian so I just asked the bus driver to tell us when to get off and where to catch the return bus. It's about an hour ride through towns, but it's scenic. It's quite a climb up a hilly driveway to the castle/winery but beautiful views. If mobility is an issue, stop in their wine store at the bus stop and perhaps someone can drive you up. We found that out after we got up there!
We left Florence at abt 8:45 am for an 11am tour and we were plenty early, but we wanted to allow buffer time for getting lost. This was living as the locals, riding with the locals.....aka through the back door. Great Day!

I took a daytrip to Ravenna from Florence and LOVED it!!! Wished I had spent the night. If you aren't interested in Byzantine churches and mosaics, this town isn't for you; but if you are, it's a must.

I'd take a day trip by rental car down to San Gimignano and down to Volterra. They're both great hill towns, and are in the same vicinity.
The roads are crooked but easy to drive to.