Honestly, having lived in SF for 9 years until relatively recently, id venture away from north beach and chinatown for food. The touristy areas tend to not be the best spots, and you'll overpay and not realize that it's nothing special. Just like pier 31/fishermans wharf. For good Chinese, go to Richmond IMHO. I lived in the Sunset, the west side of the city (and Richmond, north of the park) which is 50% Chinese, and that's where you'll get authentic stuff that isnt catering to tourists. Many don't really care much for white people, fair warning, so don't be offended if they stick you in the corner and ignore you, but it's worth it. Damn I miss the food in SF...
They're good in north beach and chinatown, just not gonna be where you find the best options, and honestly it's on par with anywhere else.