Compagnia Dei Vinattieri,located at the corner of Via della Terme and Via dei Pittori was excellent. We ate there twice in the 5 nights we were in Siena. Cappelletti was great. I had a great salume and cheese plate for lunch.
Osteria Pretto is an unpretentious little place with excellent food. Tonno di Chianti, a cold pork salad, ravioli, pici (thick hand-rolled pasta, like fat spaghetti, native to Siena). The best tiramisu I've ever eaten served in glass jars.
La Sosta di Violante a short walk from Il Campo had fried balls of pecorino in pear sauce. Even better than it sounds. My wife had spaghetti in Chianti wine sauce with pistachios and Tuscan bacon. I had medallions of beef with a mushroom sauce.
Pomodorino has meal-size salads, great pizza, and a wide beer selection. Our table on the terrace had a picture-postcard view of the Duomo at night.