This May we are staying at the Hotel Palazzo Ravizza in Siena. They do have parking. I made our reservations through booking.com. The hotel then sent me detailed instructions on how to drive directly to the hotel so that we can drop off our luggage, and then they will instruct us where to park. They also include a map. Obviously, we haven't stayed there yet so I don't have first-hand experience but the hotel looks lovely, and it was recommended to me by someone on this forum.
Just saw ChristineH's response so it was probably Christine who recommended the Ravizza to me! :-)