This article discusses one of the most important social factors of climate protection: climate concern. Most research in this area focuses on North America and Western Europe or presents international comparative statistics. Our work is innovative because we have designated a lesser-known post-socialist region in East-Central Europe as a sample area, and we intend to conduct in-depth analyses at the municipal level. Our study describes the second largest city in Hungary, Debrecen, and its agglomeration. Based on a questionnaire survey in 2020 (N = 512), we examined opinion factors, and we have presented features consistent with or different from the findings in the relevant literature. In the statistical analysis, chi-square tests and binary logistic regressions were applied to reveal significant differences between the responses of different types of respondents. As response variables, we used the questions about general concerns regarding air pollution, knowledge about climate change, beliefs about tackling, perceived threat, behavioural responses, personal actions, and demography. We found that the concern about air pollution and a feeling of threat to respondents’ life was mainly affected by the degree of climate concern. We conclude that the knowledge of local communities on climate change has increased, and risk perception has improved. Still, there is no clear relationship between the level of concern and climate-conscious behaviour. The findings provide ideas for promoting local climate management and awareness-raising in the European Union or other countries.