Hi. With over 70 school districts, I don't think you'll get a direct answer to this as it requires detail information. I do believe most of the town offer full time grade K. Here's a website I quickly searched on Google with some info all all 75 school districts. http://www.usa.com/bergen-county-nj-school-district.htm.
I have a 5 and 3 year old at home in West Milford, Passaic county, and our district started to offer full time 2 years ago. Lucky for my wife and I and just in time for my 5 year old to start.
I know this doesn't offer a complete answer, but as Peter suggested, you'll need to narrow your town search as not all towns are created equal.
Best of luck.
ARC Real Estate
North Jersey Team