Oh how fabulous that you'll have 3 nights in Siena! One of my favorite hill towns.
In Siena, I enjoyed my two-night stay at Hotel Chiusarelli https://www.chiusarelli.com/en/home/
My caveat is that I have not been there since 1998, so no recent experience; but judging from their website, it still looks lovely. It is likely still listed in the RS guidebook. The most recent Tuscany guidebook I have (2013) indicates that you can ask for a "Rick Steves Discount when you book," but who knows if that's still the case. Can't hurt to ask.
Ask for a quiet room. Near San Domenico Church (you'll hear bells in the AM), so a longer and hilly walk to Il Campo (which I felt was a plus, being further away from crowds). It's not too far from the Duomo. No matter where you stay, be prepared for lots of hills, which is part of Siena's charm. It is walking distance from the train station as I recall, which is why I chose it.
Don't rush the Duomo in Siena. If you're into it, there is so much detail to appreciate, including the mosaic tiles on the floor and many busts of the popes. Great description and self-guided tour of the Duomo in the RS guidebook.