SoHo and Tribeca (South of Hudson, and the Triangle Below Canal), aren't bad.. they are some what decriptive. (tribeca used to be the old cast iron district in NY--but many of the old cast iron building have been torn down--or stolen (but that's another story).

DUMBO ( Down Under (the) Manhattan Bridge Overpass)--is one of the stranger areas

especially since the manhattan bridge has overpasses on both the brooklyn and manhattan side--so DUMBO can reference areas in both boroughs!