The NJ Board of nursing has a list of all approved schools of nursing in the state. It all depends on what you are looking for, as there are diploma programs, associates degree, and BSN programs that all lead to eligibility to obtain a license as an RN. There are also practical nursing programs (private and public) that lead to eligibility to become a licensed LPN. While private schools may have short or no waiting lists the programs are more expensive. Public programs are often highly competitive with wait lists but lower cost. There is contact information for each school. The board of nursing also publishes the NCLEX pass rate for each program so that you can make an educated choice of where you want to go to school. Good luck.
Associate's (2yrs or so): http://www.state.nj.us/lps/ca/nursing/adegree.pdf
Diploma ('hospital based' approx 3 yr programs): http://www.state.nj.us/lps/ca/nursing/dipschool.pdf
BSN (4 yr collegiate programs): http://www.state.nj.us/lps/ca/nursing/bacschools.pdf
LPN Programs: http://www.state.nj.us/lps/ca/nursing/vocschool.pdf
Board of nursing: New Jersey Division of Consumer Affairs - Board of Nursing