Regional Innovation and Entrepreneurship Enhancement Act of 2014 - Amends the Stevenson-Wydler Technology Innovation Act of 1980 to: (1) expand the duties and reporting requirements of the Office of Innovation and Entrepreneurship, including by requiring the development of a strategic plan to guide the activities of the Office; (2) authorize appropriations for such Office for FY2014-FY2018; and (3) modify the Regional Innovation Program established by such Act to eliminate provisions relating to science and research parks and require outreach to public and private sector entities in rural communities to encourage participation in Program activities.