I would think that you can find accommodation before the Palio as you are planning. We were there in 1995 the weekend before the race and we had no trouble without reservations. I wouldn't count on that though! It's great to be there that weekend because they have practices and spontaneous marches between rival and friendly contradas.

My suggestion is to stay in the older part of town even if the accommodation isn't as luxurious.Then you get the full flavour of the event - the drums pounding andechoing through the streets, It's an amazing colourful event and we weren't even there for the race (which, I believe lasts about a minute!). We stayed at the Albergo Bernini, a Rick Steves recommendation with a rooftop terrace and dynamite views of the duomo. http://www.albergobernini.com/

Frances Toronto, Canada