Urban Air Mobility (UAM) has emerged as a promising alternative mode of urban transportation, offering the ability to bypass roadway congestion with environmentally friendly, safe, quiet, and on-demand eVTOL fleet. Our research focuses on estimating UAM demand and identifying key influencing factors using a tour-based demand model, which provides a more realistic representation of urban travel behavior. Compared with traditional trip-based models, the tour-based approach captures the interdependence of trips within a tour, thereby improving forecast accuracy for multimodal systems that integrate UAM. We apply Integer Programming (IP) to design the UAM network and estimate shifted demand, optimizing to minimize travelers' generalized costs. By modeling complete tours rather than isolated trips, the framework better reflects actual travel choices and mode-shift potential. Methodologically, building on Wu & Zhang (2021), we extended the single-allocation p-hub median problem to support a case study in the Tampa Bay Area. Results indicate that with 10 to 100 vertiports, 320 and 2,341 daily tours shift to UAM among the candidate tours. Travelers exhibit strong preferences for shorter access and egress times and distances. With the tourbased (round-trip) structure, personal vehicles (PVs) are primarily used to access and egress origin vertiports, whereas for-hire services are more commonly used at destination vertiports. Overall, the findings provide valuable insights for both city planners and UAM service providers, underscoring that UAM's success hinges on strategically located vertiports that enhance accessibility. The study highlights the importance of comprehensive, system-level planning to develop an efficient and competitive UAM transportation network.