The primary meaning of the American-English noun honky-tonk is: a disreputable entertainment venue.

I think that this word is imitative of the sound of the music heard in such venues; in my opinion, honky-tonk is simply a reduplication based on honk. An onomatopoeic noun, honk denotes:
– the characteristic harsh sound made by a wild goose (sense attested in 1813),
and, by extension:
– any similar loud, harsh sound (sense attested in 1869).

This seems to be supported by the fact that the sentence “the honk-tonk of the goose sounds from high” appeared in the Ellsworth Reporter (Ellsworth, Kansas) of Thursday 4^th April 1901. The reduplication honk-tonk was also used in An Old Horse’s Holiday, published in The New York Times (New York City, N.Y.) of Sunday 30^th July 1905:

He wandered over to Eighth Avenue, where there is asphalt for the automobilists and no grass for the out-of-date horse. The honk-tonks did not frighten him.

 

The following presents chronologically the earliest occurrences that I have found of honky-tonk and variants up to the end of 1893.

 

1-: AUGUST 1887 TO JANUARY 1893
A TEXAN WORD

 

All the earliest instances of the word that I have found indicate that it originated in Texas.

 

1.1-: AUGUST 1887
A HORSE’S NAME

 

The term appears—and this probably has nothing to do with its later use—as part of the name given to a particular horse in an article about a “splendid equine showing” at Dallas, published in The Dallas Morning News (Dallas, Texas) of Sunday 14^th August 1887:

W. T. Campbell’s stable is composed of the following stock: […] Gen. Honk-a-Tonk, b. g., breeding not known.

 

1.2-: JANUARY 1889 TO AUGUST 1890
A DALLAS THEATRICAL NAME

 

In the following from the Dallas news section of the Fort Worth Daily Gazette (Fort Worth, Texas) of Thursday 24^th January 1889, the word seems to be the name of a particular theatre:

A petition to the council is being circulated for signatures, asking that the Honky Tonk theater on Main street be reopened.

The term is defined as denoting a “variety show” in a news story published in The Dallas Morning News (Dallas, Texas) of Wednesday 6^th August 1890; “a large, black and typical southern darky with short sideburns who answered to the name of Brown” has been locked up in the calaboose after being wrongfully charged with “interfering with private property by entering the room of George Lewis”; Brown declares this to a Dallas Morning News reporter:

“[…] I came over to Dallas yesterday hunting work. […] When 6 o’clock came I went down to George Lewis’ house. […]. He lives down on the west side of south Jefferson street near the crossing of the Oak Cliff and the Santa Fe roads. […] Myself and him set and talked awhile and he got up and said he wanted to go to the honk-a-tonk (variety show).”

 

1.3-: MAY 1892 TO JANUARY 1893
THE NAME OF A DISTRICT/OF A SALOON OF JEFFERSON

 

In The Marshall Messenger (Marshall, Texas) of Friday 27^th May 1892, the word is the name of a disreputable district of Jefferson, Texas:

Jefferson, Tex., May 22.—[…]
Saturday night in the most disreputable part of town, the famous Honk-E-Tonk district, a negro attempted to rob an unknown white man, who cut out both of the negro’s eyes. The negro is named Ben McNell.
The white man struck only one lick with his knife, but it was across from right to left, and cut open both eyes of his would be robber.

However, in The Dallas Morning News (Dallas, Texas) of Tuesday 10^th January 1893, the word seems to be the name of a particular saloon of Jefferson:

Jefferson, Tex., July 9.—On Saturday night Annie Jones and Sue Williams, both colored and from Marshall, had a quarrel at the Honka Tonk saloon, which resulted in the latter’s throat being cut and the former arrested.

In the previous paragraph from The Dallas Morning News, “July 9” is a misprint for “January 9”, since the same incident was reported as follows in The Marshall Messenger (Marshall, Texas) of Friday 13^th January 1893:

A WOMAN’S THROAT CUT
At the Famous Honk-e-Tonk […].

Jefferson, Tex., Jan. 9.—[…]
Saturday night in the famous honk-e-tonk one woman drove a knife into another woman’s throat, inflicting a dangerous wound. Dr. Foster sewed up the cut. The injury party came here from Marshall. Names are not procurable.

 

2-: FEBRUARY 1893
NEW YORK CITY PROSTITUTION DISTRICT

 

In the St. Louis Post-Dispatch (St. Louis, Missouri) of Sunday 5^th February 1893, the word seems to be the name of the prostitution district of New York City:

A PARKHURST * AGENT.
Blackmailing New York’s Army of the Honk-a-Tonk in a New Way.

New York, Feb. 4.—Robert Keighton, aged 19, tried a new scheme for soliciting, or rather demanding, alms last night, which lodged him in jail for three months this morning. He went out on the streets and stopped a number of women. He told them that they were under arrest, but that for $1 he would give them their liberty. “I am,” he said, “an agent of Dr. Parkhurst’s *. There have just been 1,800 special officers appointed by him to patrol the streets and arrest all women who are out after dark. This is my beat, and I am going to pull you. Give me $1 and you can go.”

(* Charles Henry Parkhurst (1842-1933) was an American clergyman and social reformer who attacked the political corruption of New York City government.)

 

3-: APRIL TO SEPTEMBER 1893
ANY DISREPUTABLE ENTERTAINMENT VENUE

 

In The Austin Daily Statesman (Austin, Texas) of Monday 10^th April 1893, the word denotes a theatrical and gambling establishment frequented by Afro-Americans:

Brenham, Tex., April 9.—[…]
Lida Smith and Anna Chappell had a fight with knives in the Honk-a-tonk, a negro variety hall and gambling dive, at 12 o’clock last night. The Chappell woman was badly cut on the head and Lida Smith was slashed across the arm. Lida Smith is in jail awaiting a preliminary hearing.

According to The Iola Register (Iola, Kansas) of Friday 23^rd June 1893, the word came to be applied to any new low-class theatre in Oklahoma:

When a particularly vicious and low grade theater opens up in an Oklahoma town they call it a “honky-tonk.” The name didn’t “come from” anything; it just growed.

However, in the following is from The Galveston Daily News (Galveston, Texas) of Wednesday 6^th September 1893, the nature of the premises that the word designates is not specified:

Houston, Tex., Sept. 6.—The case against Special Officer Martin, charged with the murder of Henry Dixon, colored, was called before Justice Mahoney this afternoon in the criminal courtroom. […]
[…]
John Felgel testified that Dixon was running and Martin after him when the shooting occurred, and the second time he shot Dixon was falling. It was on the bridge, near the honk-a-tonk. […]
[…]
Andrew Harris testified that he was in the second story of the honk-a-tonk and saw the shooting.

(On Friday 15^th December 1893, the jury found Martin not guilty on the charge of murder.)