We've been to Florence many times, here are my suggestions. In one day you can go to Volterra and San Gimignano. In another day you can go to Pisa, and another day to Lucca.
If you really don't mind driving, in one day you can go to Cortona and Assisi. The American Cemetary in Tavarnuzze (20 minutes south of Florence) is worth a visit if you are a WWII buff, there are over 4300 American service men buried there. It is similar to the one in France.
I have some more recommendations but I'm on my tablet and it's too slow right now. I'll come back later with some fabulous shopping recs and links.
If you plan on going to Pisa and climbing the Tower, advance tickets are a MUST. Entry tickets are on a time schedule. No bags of any size are allowed, but there is free bag checking allowed 15 minutes before your entry time.
If looking for small and picturesque, would suggest Bagni di Lucca and the Devil's Bridge (Borgo a Mozzano) and then continue on to Barga and Castelnuovo di Garfagnana. If you want to go further afield, you could get a lot of recommendations for towns along the coast going north from Lido di Camaiore (Viareggio). Bagni di Lucca has literary connections and the grave of Grover Cleveland's sister who served as his first lady and who is laid under a matching tombstone at the English Cemetery next to her long-time female companion (a little bit of scandal back in the day). The Devil's Bridge is on half the postcards for sale in and around Lucca. Barga is a great little strolling town as is Castelnuovo. Look around for festivals during the time you will be there -- chestnut festivals, truffles, olive harvest, etc. all in the fall. Gallicano has a large town festival filled with choreographed dancing. Lucca hosts the largest Comic Festival in Europe at the end of October.
This may be something you’ve already experienced, but it holds beautiful memories for me. Chiantigiana car tour. SS222 from Florence takes you through beautiful villages such as Greve, Panzano, Castellina, Radda, etc. I distinctly remember the gorgeous hills of Tuscany and spontaneous picnics...not to speak of the wine.You can keep it short or continue on to Siena. This was a few years ago, and things may have changed, but it lives in my heart as a treasured memory.