Besides the spots mentioned already I'd throw in Cafe Claude, Tadich Grill and Sam's Grill, the last two being two of the oldest restaurants in California.
But SF is one of the great restaurant cities in the country. You can find great places that no one here recommends because there are just so many spots. Look at the map below, every orange dot is a restaurant, not just the ones with letters on them, the Chancellor is the purple balloon.
If you zoom back one level it looks like this.
The cluster of orange dots at Jackson & Columbia is North Beach, SF's version of Little Italy, those dots on Columbus are mostly Italian restaurants and lots, and I mean lots, of good ones; on Jackson those dots are mostly Chinese and some very good ones, it is the edge of Chinatown.
The cluster near Geary & Webster is Little Tokyo, Polk has clusters too, the Polk Gulch area has Crustacean and Swan Oyster Depot...
If you place your mouse on an orange dot it tells you the name of the restaurant and shows its Zagat rating if it has one. You can click the orange dot and it pulls up more details and sometimes the website too.