The context of the COVID-19 pandemic has brought to light the infodemic phenomenon and the problem of misinformation. Agencies involved in managing COVID-19 immunization programs are also looking for ways to combat this problem, demanding analytical tools specialized in identifying patterns of misinformation and understanding how they have evolved in time and space to demonstrate their effects on public trust. The aim of this article is to present the results of a study applying topic analysis in space and time with respect to public opinion on the Brazilian COVID-19 immunization program. The analytical process involves applying topic discovery to tweets with geoinformation extracted from the COVID-19 vaccination theme. After extracting the topics, they were submitted to manual annotation, whereby the polarity labels pro, anti, and neutral were applied based on the support and trust in the COVID-19 vaccination. A space and time analysis was carried out using the topic and polarity distributions, making it possible to understand moments during which the most significant quantities of posts occurred and the cities that generated the most tweets. The analytical process describes a framework capable of meeting the needs of agencies for tools, providing indications of how misinformation has evolved and where its dissemination focuses, in addition to defining the granularity of this information according to what managers define as adequate. The following research outcomes can be highlighted. (1) We identified a specific date containing a peak that stands out among the other dates, indicating an event that mobilized public opinion about COVID-19 vaccination. (2) We extracted 23 topics, enabling the manual polarity annotation of each topic and an understanding of which polarities were associated with tweets. (3) Based on the association between polarities, topics, and tweets, it was possible to identify the Brazilian cities that produced the majority of tweets for each polarity and the amount distribution of tweets relative to cities populations.