Sole Source Aquifer Protection Act of 1982 - Amends the Safe Drinking Water Act to provide a program for the protection of certain recharge areas overlying sole source underground water supplies. Authorizes municipalities within a sole source area to petition the Governor to designate a part of such area as a "special protection area." Requires that the petition propose boundaries for the special protection area and make certain evaluations. Directs the Governor to approve or disapprove the petition. Requires the Governor, if approving the petition, to: (1) propose the boundaries; (2) designate or establish an entity to develop a comprehensive management plan (the plan); (3) assure and encourage public participation; and (4) establish procedures for adoption and implementation of the plan. Requires the Governor, if approving the petition, to submit to the Administrator of the Environmental Protection Agency: (1) the proposed boundaries; and (2) a description of the planning entity. Directs the Administrator to approve or disapprove the Governor's submission. Authorizes the Administrator, if approving the Governor's submission, to provide such State a 50 percent matching grant for the costs of preparing the petition and developing the plan. Requires the plan to maintain the quality of the ground water recharged through the special protection area by maintenance, to the maximum extent possible, of the natural vegetative and hydrological conditions. Lists several requirements to be included in the plan. Directs the Governor to approve or disapprove the plan. Requires the Governor to consider certain factors in reviewing the plan. Requires the Governor to submit an approved plan to the Administrator. Directs the Administrator to approve the plan or to submit to the Governor the reasons for disapproving the plan. Allows the Governor 90 days after disapproval to resubmit a modified plan. Requires the Administrator to consult with the Secretary of Defense on the effect of the plan on military installations. Authorizes the Administrator, if approving the plan, to provide such State a 50 percent matching grant for the costs of implementing the plan. Prohibits such grant from exceeding $20,000,000. Authorizes appropriations: (1) for FY 1983 through FY 1985 for plan development; and (2) for FY 1984 through FY 1986 for matching grants for plan implementation. Restricts the use of such authorized funds to those activities specified in this Act.