Basic education pursues “balance” and “quality” under the premise of “universalization”. High-quality and balanced education is the general strategy of international education. We used urban network tools to measure the spatial equity of three types of basic educational facilities (kindergarten, primary school, and middle school) in the main urban area of Lanzhou City, China, from the perspective of supply and demand. This can optimize the allocation of educational facilities, and make up for the shortage of basic educational facilities. It can also provide a scientific reference and new ideas for research on public service facilities. The conclusions are: (1) The distribution of basic educational facilities presented a typical pattern of belt-shaped clusters, river trends, and dense east and sparse west. The spatial dislocation between facilities and residential buildings was significant and occurred in numerous instances. (2) The supply of basic educational facilities was weak. There were significant differences in spatial accessibility among different types and regions. The spatial accessibility of kindergartens (34.83%) was the best with regard to walking conditions, followed by primary schools (27.43%) and middle schools (21.11%). (3) The distribution of basic educational facilities was affected by factors such as historical development, natural geography, social economies, and the travel behaviors of residents; (4) It is necessary to improve the problem of spatial imbalance through the implementation of refined planning management and resource allocation of infrastructure, the construction of a “community life circle”, and the establishment of an early warning mechanism for academic degree attainment combined with big data.