New Jersey has no statewide law that says whether you can metal detect. On the Shore, the answer depends on who runs the stretch of sand, and that changes from town to town. Town beaches like Asbury Park and Cape May have no ordinance against it, though in summer you'll need the same beach badge as everyone else. The neighbors are different: Ocean Grove's beach is owned by the Ocean Grove Camp Meeting Association, and Cape May Point State Park sits two miles from Cape May's city beaches.
State land is permit-only. The State Park Service Code covers every state park, forest, recreation area, historic site and natural area the Division of Parks and Forestry runs (N.J.A.C. 7:2-1.2). Under it, "a person shall not use metal detectors or similar devices without a permit issued by the Superintendent or designee," and no permit will be issued "for use in areas of significant historical or other value" or where it would harm the resource or interfere with public use (N.J.A.C. 7:2-2.16). At Island Beach State Park the permit is free, but the natural areas that cover most of the park are effectively closed. Call the park office before you go.
Wildlife management areas run by the Division of Fish and Wildlife ban metal detecting outright. A second violation of any WMA rule costs you all sporting licenses for five years. Federal land is closed too: Sandy Hook is part of Gateway National Recreation Area, where possessing a metal detector is prohibited (36 CFR 2.1(a)(7); see our national parks guide), and national wildlife refuges such as Edwin B. Forsythe ban searching for treasure without a permit (50 CFR 27.63).