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. Grants may not be awarded after September 30, 2023. The Government Accountability Office must conduct a study on the interests, roles, and responsibilities of federal, state, local, and tribal government affected by AAM aircraft and operations.