I think it depends on the district.
DS9 is in 4th grade and he has a full day tomorrow.
DD14 is in 9th grade (High School) and she has a 1/2 day (12:30pm dismissal)
Both kids go to public school. We live in Bergen county, NJ
Unless a few have a special half day, I think they are all open. Live in the area and since most schools were closed for all/part of last week, most kids are back in school. Should be a quiet day.
We are in northeast NJ (suburb of NYC) and have a half-day tomorrow (DS is in second grade) but I think that's due to parent-teacher conferences. My good friend lives in Mount Laurel and I am pretty sure they have a regular school day.