It is about an hour by bus to Siena and that would be my choice as it drops you right in the center of the old town.
We did a day trip to Bologna this fall and I loved it but there were a lot of train disruptions and we spent over an hour waiting for a train in both Florence and then again in Bologna and the train station is a good bit from the historic center (no problem for able bodied adult but a hassle with a toddler). It is not closer or faster than Siena.
Fiesole is a suburb of Florence. You just take a local bus. I have never seen the charm. We did enjoy an opera in their amphitheater once and that was nice.