Would appreciate recommendations for a 3-star hotel in, or within a very short walking distance to, the old town center of Sansepolcro.
Go to a google Maps, zoom in the area of Sansepolcro where you want to stay, then enter HOTELS in the search box. Enter.
All hotels in the area will pop up.
Having said this, I would definitely choose to stay in beautiful medieval Anghiari instead of Sansepolcro. They are just a 5 min drive from each other.