New Jersey schools don’t get out until after June 20. (S1s graduation is June 24!). So mid-June is a good time to go to the shore. I would avoid the last week of June, as that’s beach week, especially in places like Belmar and Seaside Heights, but could be others where the kids takeover the family shore house.
Ps - ocean water temps are still around 32, so it will be a long time before they warm up this year to anything tolerable unless we get a heat wave. I’m thinking By mid-july it will be tolerable.