Smart sustainable cities represent a great challenge for the modern world. Generation Z (Gen Z), whose representatives are now entering adult life, will play a key role in the implementation of this concept. The purpose of this study is to investigate the nature of the relationship between the evaluation of smart mobility’s importance for a smart city and the attitudes and behaviours of Generation Z members in the context of sustainability, use of ICT, and their declarative and actual participation in smart-city activities. The diagnostic survey method was used to achieve the research objective. The authors designed the questionnaire based on a literature analysis. The research sample consisted of 484 representatives of Generation Z—students of universities located in a smart city, Lublin (Poland). The collected data was statistically analysed using the following methods and statistical tests: Cronbach’s alpha, Pearson’s chi-square test for independence, symmetric measures: Cramer’s V, and the contingency coefficient. The analysis of the obtained research results confirms that the conscious approach of Generation Z to sustainability has a significant and positive impact on their evaluation of actions taken in the field of smart mobility for a smart city. A similar relationship was confirmed with regard to the relationship between ICT use and smart-mobility evaluation. The significant and positive impact of young people’s participation in smart cities on their evaluation of smart-mobility solutions’ importance was not fully and unequivocally confirmed. In conclusion, the Generation Z representatives’ awareness of the importance of sustainability and caring for the natural environment was confirmed by their desire to be pro-ecological in the areas of smart mobility studied in the paper. Moreover, young people who constantly use the latest technologies see their huge potential for the development of smart mobility in cities. However, despite the growing expectations of citizens’ active attitudes and their increasing participation in smart-mobility development, it seems that the representatives of Generation Z are not really interested in it. Their declarations of willingness to join various opinion-forming and decision making processes do not actually transform them into active co-creators of smart-mobility solutions. Changing this approach can be an educational, organisational and technological challenge for smart-city authorities. The obtained research results could be used as guidelines for facilitating the search for innovative solutions in the area of smart mobility, improving the quality of life of smart-city residents based on the principle of sustainable development.