stay in chianti

Yes, doable. Pick a place that has a train to Florence. Siena would be good.

The Chianti will likely require having a car. Before recommending anything anywhere you should post here whether you plan to rent a car or not.

Can highly recommend Montepulciano. Just stayed two wonderful nights at Relais San Bruno. Definitely would need a car. Otherwise Siena is a good choice.

I did Tuscany without a car in 2015 by using the Buses and a few private drivers to towns without a direct bus to my next village. Had no issues on the buses. You can find a bus map here of the area and see which villages are connected with what bus line. You'll see Radda, Greve and Castellina in Chianti all there.

http://www.sitabus.it/wp-content/uploads/2013/03/Mappa-firenze-siena-arezzo.pdf

You can also do a bike daytrip around or a scooter vespa.

I did Tuscany without a car in 2015 by using the Buses and a few private drivers to towns without a direct bus to my next village. Had no issues on the buses. You can find a bus map here of the area and see which villages are connected with what bus line. You'll see Radda, Greve and Castellina in Chianti all there.

Robert makes a good point. We rented a car and enjoyed the freedom and flexibility, but with a little planning you could have a great time using Robert's method.

We stayed on the bus route mentioned. We actually opted to take the bus from Greve to Florence and it worked out great.

There are plenty of places to stay that are on the bus route. Radda, Greve and Castellina are all charming and have different personalities.

Montepulciano is not in the Chianti.

We have visited Chianti four times, enjoyed several places we stayed but our favorite was Panzano.