A small restaurant or diner, especially one that serves fried foods. Every time I go on a road trip, I make it a point to stop at a greasy spoon for at least one of my meals.
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]