Veterans Outreach Improvement Act of 2003 - Directs the Secretary of Veterans to establish a separate account for the funding of outreach activities of the Department of Veterans Affairs and a separate subaccount for the funding of outreach activities of the Veterans Health Administration, the Veterans Benefits Administration, and the National Cemetery Administration. Directs the Secretary to: (1) establish and maintain procedures for ensuring the effective coordination of Department outreach activities between and among such elements, the Office of the Secretary, and the Office of Public Affairs; and (2) ensure that outreach is provided in locations proximate to populations of veterans and other individuals in States that offer a high probability of improving veterans' outreach and assistance. Authorizes the Secretary to award grants to appropriate State veterans agencies for such purpose.