Sarah:
In the fall of 2007 we were in Tuscany and a couple of the guys in our group wanted to rent scooters. We easily found a place in Greve that did so. Greve is small so I would guess that there would be availability in Siena. I am sure that your innkeeper would know this information.
However, the kind of scooters they rent are for simple urban scooting around. The scooters had small engines and speed governors. Going between villages was a frightening experience as faster vehicles blew past them on the small Italian roads.
Also, remember that the "hill towns" are called "hill towns" for a reason. Those little scooters barely made it up the grade to the next village. While I remember lots of bicyclists all through Tuscany - those hills are frequent, steep and daunting - too much for this fat old man!
We all had a good laugh about it but those two fellows were relieved and happy to return the scooters. Just my two cents. Have fun.