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The rapid adoption of on-demand mobility services has brought a challenge in accessing their equity impacts at a regional scale due to the absence of consistent trip data and efficient transportation models. This study shows the potential of integrating synthetic population data and a choice-based optimization model to support large-scale mobility service region design with equity concerns. We propose a decision support tool that specifies budget-constrained optimal service regions for new mobility services under one of several objectives such as minimizing consumer surplus insufficiency. We test using New York State synthetic data and illustrate its application by considering new ride-hailing and microtransit services. The "cost of equity" is measured: under budget level II, each vehicle requires a subsidy of $71.39/day to minimize disparity and $29.86/day to minimize insufficiency. Our findings contribute to the literature by quantifying trade-offs among different services, objectives, and budget levels, thereby supporting funding and resource allocation. [ABSTRACT FROM AUTHOR]