Advanced Aviation Infrastructure Modernization Act or the AAIM Act This bill establishes a pilot grant program to support advanced air mobility (AAM) infrastructure. AAM infrastructure refers to an air transportation system that transports individuals and property between points in the United States in both controlled and uncontrolled airspace using certain aircraft, including remotely piloted, autonomous, or vertical take-off and landing aircraft. The Department of Transportation (DOT) must award planning grants for AAM infrastructure to (1) state, local, or tribal governments; (2) airport sponsors; (3) transit agencies; (4) port authorities; (5) metropolitan planning organizations; or (6) consortia of such entities. Entities that receive these grants must develop a comprehensive plan for AAM infrastructure, including vertiports (sites that support the landing, takeoff, loading, and other operations of vertical take-off and landing aircraft). Topics covered in the plan must address matters such as identifying locations for AAM infrastructure and available sources of funding. DOT must brief Congress about the plans it receives. The briefing must include an evaluation of the planned or proposed locations for vertiports and a description of best practices or lessons learned through the review of comprehensive plans. If the Federal Aviation Administration issues type certificates for at least two aircraft models designed to provide AAM transportation and other requirements are met, DOT may award construction grants to entities that submitted comprehensive plans. Recipients may use grant funds for design, environmental studies, and other capital costs related to the construction of a public-use vertiport or associated infrastructure. Grants may not be awarded after September 30, 2023.