1
general::
A cheap restaurant, especially one serving short-order fried foods. For example, College students short of cash tend to eat a lot in that greasy spoon. This expression Also implies that the restaurant is not very clean. [c. 1900]
American Heritage Idioms
2
general::
Phrase(s): a greasy spoon
Fig. a cheap diner, where the silverware might not be too clean. • The corner greasy spoon is always busy at lunchtime.
McGrawhill's American Idioms And Phrasal Verbs