Osteria Nonna Gina
Outside the Due Porte.
Osteria del Gatto
Not far from the above Nonna Gina. Menu will be in Italian but the waiters and the cooks will be available for a translation "on the fly". Fish is served one week a month. If you happen to be there in that week, don't miss the "Tonno alla Mediterranea" tuna fish in the Mediterranean way.
La Torre
This is also an excellent restaurant, in the contrada of the same name.
Osteria Sotto le Fonti
Restaurant off the beaten path, with owners who serve you personally; the waitress speaks fluently English very rare in Italy and knows how to recommend you wine, as she is also a wine tour guide. Is a pleasant walk downhill shortly outside the gates of the city, allowing you to look up at the top of the Duomo.
Nannini
A bakery/cafe with an excellent selection of Tuscan pastries: Ricciarelli, Cavalucci, Cantucci, Panforte, etc. The ingredients of same are prominently displayed in most cases, making Nannini a very attractive option to the travelling vegan.
Excellent gelato can be found just off the Campo at two gelaterias called "Il Gelato" and "Brivido". Ask for Romaney at "Il Gelato"
For something more substantial, "La Chiacchiera" next to the House of St Catherine is an excellent source of typical Tuscan cuisine; the pici thick, homemade noodles are superb.
Panforte
A unique kind of dense cake, made of honey, flour, almonds, candied fruits, a secret blend of spices, etc. tipo margherita is the classic, but several other types are made. panforte is commercially manufactured only in siena and neighboring monteriggioni, its loyal ally in medieval wars with florence. the most famous brand of panforte is sapori. you can buy panforte most cheaply in local supermarkets, but don't miss a trip to nannini on banchi di sopra see above, a pleasant caffã© where you can buy not only their panforte by weight but also many other types of unusual pastries and so forth.
Ricciarelli
Small almond paste cakes.