The COVID-19 pandemic is a global challenge, and the key to tackling it is vaccinating a specified percentage of the population to acquire herd immunity. The observed problems with the efficiency of the vaccination campaigns in numerous countries around the world, as well as the approach used at the initial stage of the National Immunization Program in Poland, prompted us to analyse the possibility of using GIS technology to optimize the distribution of vaccines to vaccination sites so as to minimize the period needed to vaccinate individual population groups. The research work was carried out on the example of Warsaw, the capital of Poland and the city with the largest population in the country. The analyses were carried out for the 60–70 and 50–60 age groups, in various approaches and for vaccines of different companies (Moderna, BioNTech, AstraZeneca), used to vaccinate people in Poland. The proposed approach to optimize vaccine distribution uses Thiessen’s tessellation to obtain information on the number of people in a given population group living in the area of each vaccination site, and then to estimate the time needed to vaccinate that group. Compared to the originally used vaccination scenario with limited availability of vaccines, the proposed approach allows practitioners to design fast and efficient distribution scenarios. With the developed methodology, we demonstrated ways to achieve uniform vaccination coverage throughout the city. We anticipate that the proposed approach can be easily automated and broadly applied to various urban settings.