This study develops a bi-objective mathematical model to determine optimal locations for Urban Air Mobility (UAM) vertiports in Seoul, South Korea. Utilizing a variety of data sources, including commercial area statistics and aviation regulations, the proposed model finds an optimal vertiport network layout for UAM service based on hub-and-spoke system. The model demonstrates a trade-off between vertiport establishment costs and logistics accessibility, with higher investments leading to improved accessibility and reduced logistics costs. Pareto optimal solutions are obtained using the ε-constraint methodology, highlighting the balance between cost efficiency and operational effectiveness in UAM network planning. The findings offer actionable insights for urban transportation planners and policymakers considering the implementation of UAM services in the near future. However, the scope of this study is limited to a specific urban context, suggesting the need for further research in diverse urban settings. This research could contribute significantly to the discourse on UAM systems, underscoring their potential in urban traffic management and mobility enhancement.