North Beach is mostly about the corner markets--quiant little stores that have been there forever--often mom-and-pop places. But if you must have a grocery store if you move there, then you can find those too. There is a much disliked Safeway supermarket on Bay Street. (It's fine and has parking too--a big plus in SF.)
If you are going to live in North Beach, however, you have to go to the corner markets--No really, its a local ordinance. "At least, twice a week all residents will help maintain the folksy, 1959 feel of the neighborhood by buying overpriced groceries from their local corner markets." (Okay, I might have made that part up.)