The topic of the COVID-19 vaccination is widely present, and, since many countries struggle with vaccine hesitancy, the aim of this study was to examine determinants of vaccination readiness. The study involved 1,769 participants (76.3% females, 23% males, and 0.7% other) age range from 18 to 77 years. Participants completed online questionnaires related to demographic characteristics, personality traits (neuroticism and consciousness), vaccination readiness scale, and two scenarios related to social relations in the context of attitudes towards vaccination. The results showed that demographic characteristics were significant predictors of vaccination readiness, where women, the elderly, the more educated, those with higher socioeconomic status, and those who were not ill from COVID-19 had higher vaccination readiness. Contrary to expectations, persons high in neuroticism and low in conscientiousness had higher vaccination readiness. Vaccine-acceptant individuals, when compared to vaccine-resistant and vaccine-hesitant individuals, had higher vaccination readiness. Regarding the scenario in which the close person has similar or dissimilar attitudes towards vaccination, the obtained results showed that the manipulation with similar/dissimilar attitude has led to the attribution of different characteristics to close persons. A close person with similar attitudes was assessed more positively than a close person with different attitudes. The results of this study support the fact that individual factors are important for vaccination readiness and that differences in attitudes toward vaccination can affect close social relations, which has not been investigated so far in the context of COVID-19 vaccination.