The COVID-19 pandemic presented the unique challenge of having to deliver novel vaccines during a public health crisis. For pediatric patients, it was further complicated by the delayed timeline for authorizing the vaccine and the differences in dosing/products depending on the patient's age. This paper investigates the relationship between the spatial accessibility and uptake of the COVID-19 vaccine in King County, WA, USA. Public data for COVID-19 vaccine sites were used to calculate spatial accessibility using an enhanced two-step floating catchment area (E2SFCA) technique. Spatial regression analyses were performed to look at the relationship between spatial accessibility and ZIP-code-level vaccination rates. The relationships of these data with other socioeconomic and demographic variables were calculated as well. Higher rates of vaccine accessibility and vaccine coverage were found in adolescent (12- to 17-year-old) individuals relative to school-age (5- to 11-year-old) individuals. Vaccine accessibility was positively associated with coverage in both age groups in the univariable analysis. This relationship was affected by neighborhood educational attainment. This paper demonstrates how measures such as E2SFCA can be used to calculate the accessibility of the COVID-19 vaccine in a region and provides insight into some of the ecological factors that affect COVID-19 vaccination rates.