We failed to write down any of the places we enjoyed eating at in Siena last year, but I did some walking around on Google Street View and looking through our photos and I tracked a few down.
San Giuseppe was indeed good although we tend to prefer more homey places. It was so funny that they provide people with miniature chairs for their bags and purses.
L'Oro di Siena --- A bit of a walk down the hill. The food was really good and interesting, but we had to suppress our giggles at the little performance the server put on to serve us our wine. Modern style not our favorite either, but, yeah, the food was memorable, especially some kind of bruschetta topping made from CELERY.
L'Osteria dei Rossi --- Simple, basic, traditional good food. If you look at the food photos on Trip Advisor you can see that this place does not pretty up the food in any way.
Osteria La Sosta di Violante --- My husband remembers really liking the more modern but not fancy food here and our photos of the food look very yummy indeed.
Osteria Enoteca Sotto Le Fonti on the Via Esterna di Fontebranda --- It's a little trek but we thought it was worth it, twice. Small family-run place. You go through a city gate (the one between the Duomo and the Saint Catherine cathedral) and down the hill past the Parking S. Caterina. The "escalator to the Duomo" helped us get back up the hill --- this escalator shows up on Google Maps and it's inside a building.
Osteria Nonna Gina --- We ate there 7 years ago but it still looked good when we walked by it last year.
See if any of these places appeal to you.