The COVID-19 pandemic has posed a huge challenge to the world in recent years. The development of vaccines that are as effective as possible and accessible to society offers a promising alternative for addressing the problems caused by this situation as soon as possible and to restore the pre-epidemic system. The present study investigated the preferences of residents in Hungary’s second-largest city (Debrecen) for the COVID-19 vaccine. To achieve this aim, a discrete choice experiment was conducted with 1011 participants, and the vaccine characteristics included in the design of the experiment were determined by qualitative methods and a pilot survey: (1) country of origin; (2) efficiency; (3) side effect; and (4) duration of protection. During the data collection at three vaccination sites, respondents were asked to choose between three vaccine alternatives and one “no choice” option in eight decision situations. Discrete choice model estimations were performed using a random parameter logit (RPL) specification with the final model extended to include a latent variable measuring pandemic awareness. The results showed that the vaccine with a Chinese country of origin is the least preferred among the respondents, while the Hungarian and the European vaccines are the most preferred. Furthermore, the increase in the vaccine efficiency level increased the respondents’ sense of utility for the vaccine; the short-term side effect was preferred to the long-term one; and the increase in the duration of protection provided by the vaccine increased the respondents’ sense of utility for the vaccine. Based on the parameter estimated for the latent variable, it can be concluded that as the level of pandemic awareness (which is more positive among people with chronic diseases and less important among health workers) increases, the choice of a vaccine option becomes more preferred among respondents compared to the “no choice“. The results of our investigation could contribute towards increasing compliance in the case of the vaccination-rejecting population, not only for COVID-19, but for any kind of vaccination procedure.