Mobility patterns have been broadly studied and deeply altered due to the coronavirus disease (COVID-19). In this paper, we study small-scale COVID-19 transmission dynamics in the city of Valencia and the potential role of subway stations and healthcare facilities in this transmission. A total of 2,398 adult patients were included in the analysis. We study the temporal evolution of the pandemic during the first six months at a small-area level. Two Voronoi segmentations of the city (based on the location of subway stations and healthcare facilities) have been considered, and we have applied the Granger causality test at the Voronoi cell level, considering both divisions of the study area. Considering the output of this approach, the so-called ‘donor stations’ are subway stations that have sent more connections than they have received and are mainly located in interchanger stations. The transmission in primary healthcare facilities showed a heterogeneous pattern. Given that subway interchange stations receive many cases from other regions of the city, implementing isolation measures in these areas might be beneficial for the reduction of transmission.