Veterans' Higher Education Opportunities Act of 2001 - Amends Federal veterans' benefits provisions to change the amount of monthly veterans' educational assistance allowance under the Montgomery GI Bill from a fixed amount adjusted for inflation to an amount equal to the average monthly costs of tuition and expenses for commuter students at public institutions of higher education that award baccalaureate degrees (75 percent of such amount for veterans whose initial obligated period of active duty is two years). Requires the Secretary of Veterans Affairs to determine such average monthly costs each year and to publish such amounts in the Federal Register.