I am sure you already mapped Chiusdino on a map and can see it is in the countryside about 27 km from Siena. You should know it is a small town, with a population of about 2000. You can get to Siena and to places nearby with the bus --- you can map them out on Google Maps and click on the public transport tab to see times.
So aside from Siena, I would suggest going to the
Abbey of San Galgano as a must!
You can also head to Massa Marittima toward the coast, and to Follonica along the coast if the weather is nice and you want to enjoy beach time. Elba is not a day trip kind of day -- especially without a car. If you want to make to Elba (it is beautiful and we always recommend it at this time as the season winds down), I would suggest moving over for at least 3 days on the island.
Assisi -- there is no easy way to get there -- with public transport, it takes an average of 7 hours because you need to pass through Florence.
As for wine tours, I would suggest contacting the Pro Loco (tourism office) in Chiusdino itself as they should be able to recommend places nearby of tour operators that operate out of the area - here's their site:
http://www.prolocochiusdino.it/
Most of the main tours operate out of Siena so your options are more limited.
In any case, you can do day trips in the area, but most will require you to take bus to Siena first and then transfer - take a look at these options:
https://www.discovertuscany.com/siena/what-to-do/day-trips-from-siena.html
For this area, we normally recommend you rent a car, it will make seeing the area much easier!