A list of "Public Deer Hunting Land in New Jersey" is available online from NJ Fish & Wildlife at http://www.state.nj.us/dep/fgw/huntland.htm
There's also information on "Lands Open or Closed to Sunday Bow Hunting" which includes Wildlife management Areas and public lands that are still closed to hunting on Sundays. The latest list I could find is from 2009 so I'm assuming there haven't been changes - see http://www.njfishandwildlife.com/news/2009/sundayhunt.htm
Of course, some of the smaller parks have no hunting allowed and those are good locations during this time too.
You can try Cheesequake State Park, Wells Mills County Park (Ocean County), the Watchung Reservation (Union County), South Mountain (Essex County), Apshawa Preserve(Passaic County) and the Ramapo Valley County Reservation (Note that the surrounding areas of Ramapo Mountain State Forest and Ringwood State Forest do allow hunting.)
For hikers, two good resources are:
- NJ Hiking http://www.njhiking.com which has specific resources for hunting season hikers
- NY-NJ Trail Conference http://www.nynjtc.org/news/deer-hunting-dates-new-york-and-new-jersey-2010