The steam train full day excursions from Siena run by Treno Natura are great fun, running through the year.
The 'Vapore' (photo) does a series of circular routes to coincide with local festivals, and there is plenty of time to hop on and off to experience local fare. Below there are links to the calendar/timetable (just click on a date for full details and fares), and a separate link with a little more information.
*Apartment Holidays in Chianti*
Siena Steam Train Breaks
Spring 2016 dates available very soon
Click on the 'timetable' link above for full itineries. Fares are typically 35 euros pp, with children under 10, free.