A “greasy spoon” (formerly called a “dirty spoon”) is an eating establishment that is unsanitary or one that serves inexpensive and often fried foods to working-class customers. A New York City restaurant called the “Dirty Spoon” was cited in the New York (NY) Times in 1866. A saloon called the “Greasy Spoon” was cited in print in 1897.
 
By the 1910s, both “dirty spoon” and “greasy spoon” were used to describe the same type of eating establishment. “Dirty spoon” quickly fell into disuse—perhaps because “greasy spoon” sounded more appropriate, or because dirt is more naturally associated with a shovel than with a spoon.
 
   
Wikipedia: Greasy spoon
Greasy spoon is a colloquial term used in Britain and North America for archetypal working class eateries. The name “greasy spoon” is used to imply a less than rigorous approach to hygiene and dishwashing, and appears to date from 1925.
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United States
Many typical American greasy spoons focus on fried or grilled food, such as fried eggs, bacon, burgers, hot dogs, hash browns, waffles, pancakes, omelettes, deep fried chicken and sausages. These are often accompanied by baked beans, french fries, cole slaw, or toast. Soups and chili con carne are generally available. A full meal may be available for a special price, often called a “blue-plate special”. A typical “blue plate special” might include a slice of meatloaf, mashed potatoes with gravy, a cooked green vegetable, and a dinner roll. Regional fare is often served. Coffee, iced tea and soft drinks are the typical beverages, and pie and ice cream are popular desserts.
 
Greasy spoons are regionally called diners in the Northeast, cafes elsewhere. Diners were originally prefabricated, and some were made to look like railroad dining cars. Diners are generally characterized by a casual atmosphere, a counter, and late operating hours.
   
wiseGEEK
What is a Greasy Spoon?
Greasy spoon is a term used both in the UK and the US to denote a type of restaurant that serves typically simple food, often grilled or fried. In the UK the greasy spoon would likely serve varieties of pub grub, like sausages, fish and chips, and baked beans, and would probably be located in low to middle class neighborhoods. The food is not known for its quality, but more for its relatively cheap cost and large portion size. In the US, the greasy spoon is a staple throughout much of the country and may be synonymous with the term truck stop, even if truckers don’t frequent the restaurant.
 
The term greasy spoon dates back to the early 20th century and has a couple of implications. First it implies that a lot of greasy and fattening food makes up most of the menu. Second, it suggests that hygiene may be an issue and things like silverware can be improperly washed. This is not always the case, especially with the advent of modern restaurant dishwashing equipment and laws governing food preparation and safety. The modern version of this type of restaurant can be very clean and nice, but prides itself on serving grease-laden types of food that are beloved by many.
 
Dictionary of American Regional English
greasy spoon n. Also greasy kitchen, ~ skillet; for addit var see quot 1965-70. Also called grease pot.
A small, cheap restaurant that usually serves food of poor quality.
1925 Writer’s Monthly June 482/2 (OEDS), Greasy spoon, a low-class restaurant.
 
(Historical Dictionary of American Slang)
greasy spoon n. a small cheap restaurant or lunch counter, esp. one specializing in short-order fried foods.
1918 Mayo Trouping for the Troops 88: At the foot of the hill…was a little black “lean-to” called “The Greasy Spoon.”
1925 Writer’s Mo. (June) 486: Greasy spoon—A low-class restaurant.
1943 J. Mitchell McSorley’s 74: For a time Gould haunted the all-night greasy spoons in the vicinity of Bellevue Hospital.
1948 Chaplin Wobbly 68: The rancid smell of beer and frying hamburgers from a nearby “greasy spoon” eating joint did things to my stomach.
   
(Oxford English Dictionary)
greasy spoon (restaurant) slang (orig. U.S.), a cheap and inferior eating-house
1925 Writer’s Monthly June 486/2 *Greasy spoon, a low~class restaurant.
1951 Time 31 Dec. 29/2 They [sc. the Marx brothers]..ate in coffee pots and greasy spoons.
1966 C. HIMES Heat’s On iii. 25 A room behind a greasy-spoon restaurant. Ibid., The cook came from the greasy spoon.
1968 L. DEIGHTON Only when I Larf viii. 110 Bob said he was hungry and wanted to pull up at every greasy spoon we passed.
 
26 February 1866, New York (NY) Times, pg. 8:
Last evening, at about 10 1/2 o’clock, Officer OATES, of the Fourth Precinct, discovered a fire bursting out through the window of the second floor of the two-story frame building No. 59 Cherry-street, formerly enjoying the name of “The Dirty Spoon,” but latterly occupied by TIERNAN & CO., dealer in cottons,...
 
23 May 1879, New York (NY) Times, pg. 8:
Capt. Petty and a squad of his officers had early in the morning raided a low lodging-house in Oliver-street, kept by Mrs. Bridget Donnelly, and known as “The Dirty Spoon.”
 
24 August 1897, St. Louis (MO) Republic, “Warring Saloons on the Levee Reduced the Price of a Drink of Whisky,” pg. 5:
The fight was started about noon yesterday by a saloon which is known to the roustabouts by the euphonious title of “The Greasy Spoon.” The saloon bears no sign of any description over its door, yet the “Greasy Spoon” is well known to all the deckhands on the river.
   
16 April 1899, Washington (DC) Post, pg. 24:
” .... Who went kiting’ [sic] out t’ th’ track last Saturday with a whole lot o’ friends’ dust just f’r the sake o’ blowin’ it on one o’ the greatest runners in training, the mare Imp, t’ see her beat a furlong by a 50 t’ 1 crab, an’ th’ sensation plug Imp not one, two, three, in a field o’ five? Why, you, you mutt-head, an’ the likes of you. (...) After the show I walks down t’ th’ Dirty Spoon restaurant with one o’ my two-bit pieces in my mitt t’ git some pork chops, fried potatoes, an’ a cup o’ coffee, an’ on my way there I seen these wise gazebus o’ bookies step out o’ calashes and walk into th’ crack eatin’ joint o’ town.”
 
Chronicling America
24 February 1901, San Francisco (CA) Call, “Whare San Francisco’s ‘Bohemia’ Dines,” pg. 9, col. 5:
Among others that deserve honorable mention are “The Dirty Spoon Restaurant,” ‘The Flytrap,” “The Silver Moon” and “Mary’s Little Lamb.”
   
20 May 1902, Nebraska State Journal (Lincoln, NE), pg. 10, col. 3:
Peter Christiansen, who rooms at the “Rusty Shovel” on North Sixteenth street and who said he took his meals at the “Greasy Spoon,” in the same locality,....
 
16 December 1908, Syracuse (NY) Herald, pg. 7, col. 7:
Turtle meat is now served at the poor farm and it has a place on the daily bill of fare at the Greasy Spoon restaurant in Alton. (Illinois—ed.)
   
11 September 1909, Kansas City (MO) Star, pg. 8:
After a curbstone meditation he decided to toss the dime. If it fell heads he would purchase a stack of wheat cakes at the “Sign of the Greasy Spoon” nearby. It it fell tails he would invest in “rough-on-rats” and end it all.
 
13 May 1910, Muscatine (Iowa) Journal, pg. 8, col. 1:
Maison privee the rascal called it, to dodge the exciseman and his licenses; and “The Dirty Spoon” is what some chorus girl nicknamed it on a happy night.
     
Chronicling America
23 May 1910, Salt Lake Herald-Republican (Salt Lake City, UT), pg. 4, col. 3:   
Scorning the germless pie, the pasteurized coffee and the boiled ham, Doc Wiley generally walks a half mile from his office to an obscure little eating house. Its patrons speak of it as “The Dirty Spoon.” (...)—Washington Times.
   
Chronicling America
15 October 1910, Washington (DC) Times, pg. 6, col. 7:
They simply pour boiling water over the leaves and almost immediately fill the cups with this beverage which scientists have pronounced as slightly exhilarating, but harmless—a process unfamiliar in quick luncher, “dirty spoons,” and even higher grades of American restaurants,...
 
21 January 1912, Atlanta (GA) Constitution, pg. 3B?, col. 2:
No matter what the time of day, be it morn or eve or noon
You can gently lead him by the hand, to the “sign of the greasy spoon,”
And he’ll face a meal of onions, beef steak, and hay and cream
And a hundred Mamie-Taylor’s to the scandal of Joe Bean.
(...)
—SIS FALVEY.
December 17, 1911
 
25 February 1912, Fort Worth (TX) Star-Telegram, pg. 6:
Comes now the “potato king”—a very interesting person since the baked spud the size of a buckshot is priced at a dime, even in greasy spoon restaurants.
 
18 February 1914, Duluth (MN) News-Tribune, pg. 8:
He eats his lunch in the greasy spoon hangouts with the rest of the bunch and, to make a long story short, is a regular fellow.
   
15 March 1915, Indianapolis (IN) Star, pg. 6, col. 3:
Signs We Never See.
“Eat Here at the Sign of the Greasy Spoon. The Most Insanitary Restaurant in the City.”
   
18 March 1922, Olean (NY) Evening Herald, “Gladys Walton in ‘The Wise Kid’ at the Strand Theatre,” pg. 8, col. 4:
As “The Wise Kid” Miss Walton presents a little different characterization. She is the cash register queen in a New York restaurant a shade above the “greasy spoon” establishments in quality of food and patrons.
     
Google Books
Adventures of a Scholar Tramp
By Glen Hawthorne Mullin
New York, NY: The Century Co.
1925
Pg. 160:
It was in a cheap little hole in the wall which Jersey was acquainted with and which he called the Dirty Spoon.