Rural and Urban Health Care Act of 2001 - Amends the Immigration and Nationality Act to: (1) revise admission requirements for nonimmigrant alien nurses, including increasing the type of qualifying employer-facilities; (2) revise related immigrant status provisions; and (3) increase the number of annual two-year foreign residency requirement waivers for aliens receiving graduate medical education or training in the United States.

Directs the Secretary of Health and Human Services to award grants to States, local governments, and institutions of higher education for recruitment and training of domestic registered nurses and other health care providers.