If I had just one place to eat in San Francisco, it would probably be Little Joe's, now at about 5th and Mission. Best Veal Parmigiana in the world. Their Cacciucco is also amazing if you love seafood (think clams, mussels, crab and other shellfish in a garlic tomato soup). They also supposedly have the best meatballs in town. Inexpensive.
If I had two, I would add Scoma's. Great, fresh seafood in a classic setting on the docks in the back of Fisherman's Wharf. Expensive, but cheaper at lunch and waaay worth it. Especially if you love crab. You can get a prix fixe meal, consisting of Crab Louie (or another classic entree), Clam Chowder, a dessert, and all the sourdough bread and butter you can eat for about $23 at lunch. Or, if you're a real crab lover, for a splurge go for their garlic and olive oil roasted crab, served hot in the shell.
If you don't care about atmosphere, Swan Oyster Depot on Polk St. is much cheaper and has the freshest seafood in town (they supply many of the local restaurants), served up on a crowded lunch counter (no dinner). There's usually a line to sit down, because all the locals know about that place. Inexpensive to Moderate.
If I had three, I probably would do Dim Sum at Gold Mountain, on Broadway near Columbus. Classic, fresh and delicious authentic Dim Sum and almost the entire clientele is composed of local Chinese residents. Moderate.
For a real experience, take your life in your hands and eat the best hamburger in town at Original Joe's in the Tenderloin. Go at lunch only -- not after dark. They have their own in-house butcher, so the hamburger is extremely fresh, and really good. Cheap, too.
Maybe a dessert at Max's Opera Cafe at Van Ness and Golden Gate. A seven-layer cookie (two of the layers are ice cream and hot fudge) would fill the bill, and the waiters/waitresses are show people who get up and perform through the night. Moderate.
Further up Van Ness, at Geary, Tommy's Joynt is a classic Hofbrau with about a hundred different beers, and quite a few on tap. Go for the classic Turkey Leg or some kind of Roast Beast sandwich/entree. Or be a little adventurous and try the Turkey Sloppy Joe (good, and cheap), or the Buffalo Chili. Inexpensive to Moderate.
But SF is particularly known for its Seafood, Italian food and Chinese food.
Or just look at my TUG Dining Guide to San Francisco. It's now about two years old, but many of the recommendations are still valid.