there are so many! Here are a few
Bell Tower (at Jackson I think): Great atmosphere and GREAT food, great service. One of my favorites!
Polkers(around Green) great Burgers and salads, not to mention the fries!Also this is the place if you love pancakes.
Little Thai (at Broadway) yummy
Cafe Rex (near Vallejo) yummy cafe style, also good for breakfast.
Victors (near Pine) great thin pizza, pasta here is so-so.
Now for some not on Polk:
Nob Hill Cafe (Jones/Clay?) delightful neighborhood Italian spot with hard to beat atmosphere and great food too!
Janya Thai Kitchen (Larkin/California) really good and fresh food.
Yu Lee (Hyde/Jackson) by far the best pot stickers in town. This place is a Chinese gem.
there are so many more, try them all. What a great neighborhood to live in!! You are lucky!