We've stayed at Il Ciocco just outside Barga ourselves and it is a great place!
It is in the middle of the countryside in an area known for its outdoors activities -- we went hiking up over Gallicano and Fornovalasco on the CAI trails up to Monte Forato, another time we went back to the same area but to visit the
Wind Caves/Grotta del Vento
Another day we just drove around and wandered to the Devil's bridge, to Bagni di Lucca and to the small towns in the area, including Barga, of course!

You can see more of what's in the area here:
https://www.discovertuscany.com/garfagnana/
If you haven't been to
Lucca, and are not keen on hiking, then I'd likely do a day trip there instead ;-).
I agree, once you're in Florence, I'd suggest returning the car -- you'll only be paying for having it parked somewhere, and parking is not cheap in Florence either. Otherwise if you haven't yet booked a place, as long as you stay out of the center and the place has parking, you could keep it and do day trips into Chianti as well as to San Gimignano and Siena. 3 days will fly by, I do recommend you enjoy them in Florence but if you want to add anything else, you'll need to do it then. If you already have a place and it is downtown, better no car -- and do a day trip with a guided tour, such as a
wine tasting to Chianti or a
day trip to Siena and San Gimignano.
Take a look at the links to see options ;-)