A deli, a diner, and a steakhouse. There, that should cover it 
I wasn’t really kidding about the 3 above, it’s a good cross-section of New York and Americana both.
Aside from those and pizza:
Soul food: Sylvia’s or Charles (new location too)
Italian American / Red Sauce: Go big like Carbone, or a bit less at one of the places on listicles (Don Angie, Frankie’s, etc), or get a decent but convenient version somewhere like Parm or Meatball Shop or then any neighborhood pizza and pasta shop.
Chinese American: I think this is pretty distinct from chinese elsewhere
