What Jersey does have is diners. You've seen pictures of the chrome and enameled-metal Art Deco beauties that are, classically, diners. Those are diners, sure, and happily a lot of them are being restored. The menus at diners vary, but the conventional wisdom is that you can expect to find ridiculously varied choices that go on for many pages. Some diners are known for their matzoh ball soup and other Jewish specialties.
Diners often are open late, or around the clock.
Diners are an authentic piece of Jerseyana, and if you come to visit, you owe it to yourself to eat in one at least once.