Ciao Sarah,
While January 6 is a holiday and many places will be closed, there will still be some restaurants and museums open for eating and visits. San Gimignano and Siena are particularly important for tourism, so both have a general greater number of places open than the smaller towns. Expect many shops and grocery stores to be closed, but also expect to find coffee shops and restaurants open.
Since you arrive on the 5th in Siena, make sure to ask where you're staying at - they'll likely know of special events tied to the Epiphany you can also take part of, as well as restaurants or other places nearby that are open for sure on the 6th. Then you can decide what to do on the 7th, if you want to head to San Gimignano then or not... I'd say it is likely you'll find a good amount to do regardless.