Cost of New Jersey Assisted Living Facilities. According to the 2015 Genworth Financial cost of care survey, the average cost of assisted living in New Jersey is $5,725 per month. The monthly base rate for New Jersey assisted living is typically higher when compared to neighboring states.New Jersey is also more expensive compared to the national average.This cost is the base cost for a one-bedroom assisted living unit in New Jersey. Additional fees beyond the base rate may apply.he monthly base rate for New Jersey assisted living is typically higher when compared to neighboring states. New Jersey is also more expensive compared to the national average. This cost is the base cost for a one-bedroom assisted living unit in New Jersey. Additional fees beyond the base rate may apply.