I can only offer my personal experience. I want to immediately state that my opinion is based on my husband and I not doing well in shoulder-to-shoulder crowds. I have a disability, and absolutely can't be bumped or chance tripping in a crowd. We spent two weeks in Tuscany/Western Umbria at the end of last Sept. 2017.
On our way to Siena, we were hoping to stop in San Gimignano. We never even entered the walls of San Gimignano........As we approached the parking lots outside the town, there were "Full" signs posted, partially due to numerous buses. We decided to keep on driving. Great decision.....We ended up in Volterra on "market day". We had such an enjoyable lunch and afternoon in Volterra!
After Volterra, we were on our way to spend a few nights in Siena. However, after just one evening/early morning, we decided to leave. It was sooo incredibly crowded, we couldn't even walk. We were herded through the streets from the momentum of the crowds. One tour group after another, vertical pole w/flag attached, shuffled along, taking up entire widths of paths. Because Siena is a walled town, there isn't anywhere for crowds to dissipate. (Even though Siena has a huge piazza.......It, too, was packed.) In 2016, we visited the Vatican. Even the Vatican wasn't as crowded as Siena. This was incredibly disappointing. So we left Siena before lunch, and returned to Volterra for another excellent lunch and relaxing (and interesting) afternoon.
I'm happy to say that in every other town we visited, there were no crowds. Florence, Orvieto, Montepulciano, Pienza, Assisi, Spoleto.......Not a single tour group or obstructed street. The difference between Siena and the other towns was like night and day.
I would hope that, by going in October, the crowds in Siena might be lighter? But I wouldn't be surprised if that isn't the case, given that Oct. & early Nov. are usually times of the grape & olive harvests. I can't imagine what it's like during the Palio. Perhaps someone has had a better experience in Siena, and can provide advice as to how/when to navigate the crowds? Clearly, my husband and I don't do well w/crowds, and try to avoid them. We had originally planned to make Siena our home base for the week.......For us, we're happy that we changed those plans. But we have friends who say that Siena is their favorite Italian hill town in all of Italy. So if you're comfortable navigating and touring in crowds, you will probably have a quite different experience.