Ciao esmith,
I am assuming you want to stay pretty central in the historical center, correct?
In Siena, we have stayed at the
Locando San Martino and it had an elevator. It was a great location on a street off the Piazza del Campo so very central... and I remember there were no hills to go from there to the Campo. If you arrive with a car, they don't have parking but will tell you how to get to them to do luggage drop off.... wherever you stay, mention these needs and get more details.
Last summer when I was almost 8 months pregnant we stayed at
il Chiostro del Carmine and that was tough for me, there was a lift along the stairs the type added on to use for wheelchairs but it wasn't useable by just anyone. I took the stairs very slowly to our first floor room and was out of breath by then, as you can imagine, so I'd leave this one off the list.
Unfortunately it is hard to search for this service but here are a few more I found that might be good for you:
Jolly Excelsior
Hotel Minerva
Hotel Duomo
As far as stairs to the front door - it is likely that some of the old palaces might have a few stairs but generally these are more just like a few steps, never an entire floor amount. The elevators are only used by guests who need them, and are often quite small as they were added in whatever space was available so I wouldn't worry about them being busy.... but if they break, that is something I am sure they would fix quickly. I wouldn't worry about that eventuality - but when you book, DO mention that the lift is very important for your stay and that either they make sure it is functional for your arrival or they offer ground floor rooms. That might be a possible solution in several of these hotels. If they can't assure you of one or the other, I'd select a different hotel.