Shared Autonomous Electric Vehicles (SAEVs) are pivotal for future transportation, offering both promise and challenges upon integration with the power grid. This symbiosis augments power system flexibility, stability and reliability through Vehicle-to-Grid (V2G) services, and optimize transportation efficiency. However, it amplifies the demand for robust charging infrastructure and electricity power during peak periods. This paper proposes a framework employing a sequential receding horizon optimization approach to manage SAEV mobility and charging dynamics. Focused on maximizing transportation service quality while ensuring power grid stability, the model accommodates dynamic trip requests and electricity generation, utilizing a rolling horizon algorithm. Notably, the study explores the potential of SAEVs in fortifying the integration of renewable energy resources (RES) into the power grid. Our research strives to equip policymakers and system planners with a robust tool for crafting efficient and sustainable future urban transportation and energy systems.