Humphry Slocombe is essential for some of the best ice cream you'll ever have. I recommend the Secret Breakfast, a staple of their selection. They have new stuff all the time though.
http://www.humphryslocombe.com
There are countless restaurants in "The City", so I won't bore you with a big long list, but I will say that La Mar on the Embarcadero had some of the best Peruvian food I've ever had, or really just some of the best food I've ever had. Ceviches and Causas are must haves.
http://lamarsf.com