Hey there, made an account just to reply to you :) long time lurker.
We were fortunate enough to be in the area in 2019 and decided to stay in Siena. I think staying in Siena was the right call so we were not rushed out of there trying to catch the train back to florence.
If you actually want to see the event, you have two options.
somehow buy a bleacher seat, i think they are expensive and you have to search hard and buy early.
or stand in the center for free.
We stood in the center for free for about 5 hours. once your in the middle you cant really leave until the event is over. (no bathrooms). At a certain time they close the center and you cant go in or out. but i would expect to be in the center for 3-5 hours with A LOT of people. but thats was kind of part of the thrill for us. We were there in July and it was HOT.
you could also choose to watch on a tv in a local bar and go out in the streets before and after.
The horse race itself wasnt too exciting in my opinion, my wife loved it. it only lasts a few minuets but the parade before last well over an hour. The real excitement for me was watching the local people be so passionate about it and parade through the streets before, during and after.
I dont feel the need to see it again, would actually like to see Siena not during the palio because im sure its quite different. But i wouldnt take back our experience for the world.
I would say that if you dont like heat and big crowds, then dont go out of your way to see it, but if you happen to be near the area during that time, then get a place in Siena for the night and see it. Truly could be a once in a lifetime oppurtinity.
hope that helps.