I am not sure about "the cheapest," but Bakersfield College (BC) in Bakersfield, CA has a Registered Nursing program where one can earn an Associates Degree: http://www.bakersfieldcollege.edu/
"The Bakersfield College Allied Health Division offers Associate of Science degree programs in Radiologic Technology and Registered Nursing and a certificate program in Vocational Nursing. Certificates of completion are offered for Emergency Medical Technology and Nurse Assistant."
Because it is a public community college, it is very inexpensive. Student who graduate from BC often transfer to Cal State Bakersfield to get their Bachelors degree: http://www.csub.edu/nursing/