7 day unlimited ride Metrocard - $32
http://web.mta.info/nyct/fare/FaresatAGlance.htm

Weekly (Unlimited trips between two rail stations from 12:01 a.m. Saturday through 6:00 a.m. on the following Saturday) NJTransit between Newark Penn - NYC $46.50
http://www.njtransit.com/pdf/rail/R0070.pdf

See PATH info here for an alternate to NJTransit between Newark and NY depending on when and where you want to go.
http://www.panynj.gov/path/fares.html