Neighborhood Access and Equity Grants Act This bill establishes discretionary grants for removing, replacing, or retrofitting highways and freeways to improve connectivity in communities and for planning and capacity building to increase community involvement in transportation planning and related activities. The bill prioritizes grants that fund projects in economically disadvantaged communities or that meet other criteria. The Federal Highway Administration (FHA) must award the grants to state, tribal, territorial, and local governments and metropolitan planning organizations. For the planning and capacity-building grants, the FHA may award grants to nonprofits or institutions of higher education that partner with governments or metropolitan planning organizations.