I am considering Yale and USC after I complete LVN-BSN with National. Here is what Yale says:
Requirements for admission for registered nurses include a baccalaureate degree from an accredited college or university and graduation from a school of nursing (approved by the licensing board of the state in which it is located).
Usually under admission requirements, the accredidation needed will be explained. There is no such thing as accredited enough or not. It's either accredited by an acceptable accrediting body or it isn't. National is an accredited university same as Point Loma Nazarene, USD, SDSU. Here is the site to check CCNE accredidation:
http://www.aacn.nche.edu/CCNE/reports/accprog.asp
National University
La Jolla, CA
Accredited nursing degree program: baccalaureate
Date of last review for baccalaureate: November 13, 2000
Baccalaureate program accredited through: June 30, 2011
Initial baccalaureate accreditation action: April 21, 2001
Most recent baccalaureate accreditation action: April 21, 2001
Next baccalaureate review: Fall 2010