It has been widely recognized that public parking, if not managed correctly, can significantly decrease a city’s quality of life due to increased traffic and its impact on mobility and the environment. To avoid these negative effects, various parking policies have been proposed to reduce traffic while guaranteeing high accessibility, especially in city centers. This work investigates different pricing policies for public parking, including dynamic pricing and Machine Learning-based strategies that can directly optimize policy goals, such as improving mobility or accessibility. In doing so, we pay special attention to an aspect often ignored when implementing pricing policies for public parking: fairness with regard to equal outcomes for different social groups. Since the effects of pricing policies are very sensitive to financial inequality, we specifically investigate the impact of policies on different income groups. As a foundation for these experiments, we introduce a parking simulation featuring an empirically calibrated behavioral model of parking. We find that (1) dynamic pricing schemes may negatively impact fairness; (2) fair pricing for parking may require different fees for individual social groups; (3) focusing on single policy goals when devising pricing for parking results in unintended consequences; (4) Machine Learning shows potential for creating pricing strategies combining different policy goals.