The CPS is nationally representative, representative at the state level, and also representative at some large sub-state areas. The Census Bureau states that “The CPS data provide reliable estimates at the state level, and for 12 of the largest metropolitan statistical areas.” It is not clear which 12 metropolitan statistical areas they refer to. However, some areas in New York state and California are independently sampled, meaning estimates from those areas are representative. You can read more in the CPS Technical Paper 77, specifically page 52.
“The CPS sample consists of independent samples from each state and the District of Columbia. Each state sample is specifically tailored to the demographic and labor market conditions that prevail in that particular state. California and New York State are further divided into two substate areas that also have independent designs: Los Angeles County and the rest of California, New York City and the rest of New York State. Since the CPS design consists of independent samples for the states and substate areas, it is said to be state-based.”
Census Bureau documentation suggests that estimates for some metropolitan areas, metropolitan divisions, and central cities are representative of those areas. In CPS Technical Paper 66, the Census Bureau writes:
“Annual averages from the CPS for the four census regions and nine census divisions, the 50 states and the District of Columbia, 50 large metropolitan areas, and 17 central cities are published annually in Geographic Profile of Employment and Unemployment.”
In the Geographic Profiles of Employment and Unemployment 2015 to present, I only see tables by census region, division, and state, but for some earlier years there are tables for a number of sub-state areas. The 2010, 2011, 2012, 2013, and 2014 profiles include estimates for “54 large metropolitan areas, 22 metropolitan divisions, and 41 principal cities.” This suggests that estimates for San Francisco may be representative of San Francisco in some years (and likewise for some other sub-state areas), but I am not able to find definitive information from the Census Bureau on the topic by year or for more recent years than 2014.
I would caution you about restricting your analytical sample too much (i.e., by studying a very specific population within San Francisco). Pooling multiple samples (e.g., data from multiple months or years) will provide you with a larger sample size that is more likely to be representative. As always, you should refer to what people in your field have done or recommend for analysis of CPS data at sub-state levels.