I second Aziza, definitely. Acquerello is perhaps the best Italian food I have ever had, barring meals in Italy. Very romantic as well. Cafe Claude if you're downtown and want a lovely bistro lunch. Medjool if you want nummy pan-Med small plates, cool cocktails and lots of eye candy. Limon for the ubiquitous Peruvian, but Destino is a good fallback if you cannot get in.
As a Bay Area native and former SF resident now living in LA, I would encourage you to seek out the following places, which I think we have nothing like:
Betelnut - Pan Asian (not Japanese fusion, like most in LA) - get the green papaya salad and chile fried calamari and try other stuff
Delfina - California meets Italian sensibility
Farallon - grab lunch there in the main dining room - there's no room like it in LA and the food is great.
Zachary's pizza in the Rockridge area of Oakland, you can take Bart from SF - 10 minutes - get the chicken and basil stuffed pizza. Again, nothing like it in LA.
Ferry Building on Saturdays (arrive by 10am latest) for great fruits, produce, breads, sandwiches, coffee, etc. There are lots of tastings offered and great brunch to be had. The Fatted Calf is great for sausage, bacon, and pate.
Koi Palace. The gold standard for dim sum in SF even though it's in Daly City. Better than anything I've had in LA or NYC.
Canteen. Only in SF. Young, inspired chef, Dennis Leary gives up fine dining to serve his brand of cal-cuisine from a cute diner-like restaurant. The dinner brioche rolls are amazing. The beef hash for breakfast is perfect. I rented a hotel nearby just so I could stay overnight and do both dinner and brunch there. I have not been post renovation.
Santa Japanese Restaurant. In San Mateo. My hands-down favorite for tonkotsu ramen. Go during dinner for great chicken kaarage. Beware, the lines are long and he stops serving ramen when they run out of noodles...probably because gluttons like myself like to ask for extra noodles.
Chez Panisse or Oliveto if you can make it out to Berkley. Zuni if you cannot.
Redd if you can make it out to Napa.