The term “Big Apple” usually refers to the racetracks of New York City (and, by extension, the city itself), but the racetrack term sometimes includes the Saratoga Race Course at Saratoga Springs, New York. John J. Fitz Gerald’s “Around the Big Apple” column on February 18, 1924 in the New York (NY) Morning Telegraph included the graphic of an apple with New York City’s skyline and the words:
 
“The Big Apple. The dream of every lad that ever threw a leg over a thoroughbred and the goal of all horsemen. There’s only one Big Apple. That’s New York.”
 
“Big Apple” originally referred to the New York racing circuit of Belmont Park, Aqueduct Racetrack, Jamaica Race Course (demolished in 1959), Empire City Race Track (now Yonkers Raceway & Empire City Casino) and Saratoga Race Course.  “Of the five tracks that constitute what the boys are pleased to term the ‘big apple’ Empire City and Saratoga are the only ones that retain this vestigial” was printed in the Brooklyn (NY) Daily Times on August 15, 1927. Two of these five tracks (Empire City and Saratoga) are clearly not in New York City, and Belmont Park is just east of the New York City line in Elmont, New York (Long Island).
 
An article in The Saturday Evening Post in 1927 includes Saratoga:
 
“For one thing, I’m getting my chance at last for to do my stuff up there on the Big Apple; and, believe it, I am going to show the folks around Belmont and Aqueduct and Saratoga some race riding as really is race riding.”
 
A 1928 New York (NY) Morning Telegraph column titled “On the Big Apple” included articles from Aqueduct, Belmont, Empire City, Jamaica and Saratoga. “On The Big Apple: Snappy Chips from Saratoga” was a column title in August 1928.
 
A 1947 article titled “The Boys on the Big Apple” in Harper’s Bazaar included more race tracks:
 
“But that’s when they are on ‘The Big Apple,’ which is the jockeys’ name for the circuit which includes the big and fashionable tracks — Belmont, Saratoga, Hialeah, Santa Anita, and a few others.”
 
“Big Apple” did not include Saratoga, Hialeah or Santa Anita in the book Fabulous Bawd; The Story of Saratoga (1952) by Mel Heimer:
 
“They follow the sun to Hialeah and Santa Anita in the winter and up through the Big Apple of the New York tracks in the summer, chasing the buck grimly and doggedly — and then they come for a month to Saratoga and they slow up a little and become, for a moment, the improvers of the breed.”
   
   
Wikipedia: Saratoga Race Course
Saratoga Race Course is a thoroughbred horse racing track in Saratoga Springs, New York, United States, with a capacity of 50,000. Opened in 1863, it is the third oldest racetrack in the US (after 2nd oldest Pleasanton Fairgrounds Racetrack & oldest Freehold Raceway), though it is often considered to be the oldest sporting venue of any kind in the country.
   
Newspapers.com
15 August 1927, Brooklyn (NY) Daily Times, “Added Money Is Favored Over Guaranteed Stakes” by John H. Lewy, pg. 2A, col. 5:
The Metropolitan Jockey Club, Jamaica, scrapped them all this year (guaranteed stakes—ed.), and the Queens County organization, Aqueduct, followed the lead set by Belmont Park. Of the five tracks that constitute what the boys are pleased to term the “big apple” Empire City and Saratoga are the only ones that retain this vestigial.
 
Google Books
The Saturday Evening Post
Volume 200
1927
Pg. 14:
For one thing, I’m getting my chance at last for to do my stuff up there on the Big Apple; and, believe it, I am going to show the folks around Belmont and Aqueduct and Saratoga some race riding as really is race riding.
 
15 June 1928, The Morning Telegraph (New York, NY), pg. 18, col. 4:
On the Big Apple
ACTIVITIES AT ANCIENT AQUEDUCT
(A different sub-head was used for various other tracks, such as Belmont and even Saratoga. No authorship of the column was usually given, probably indicating that it was written by John J. Fitz Gerald.—ed.)
 
31 July 1928, The Morning Telegraph (New York, NY), pg. 8, col. 1:
On the Big Apple
SNAPPY CHIPS FROM SARATOGA
     
Google Books
Harper’s Bazaar
May 1947
Pg. 235, col. 1:
THE BOYS ON THE BIG APPLE (by John McNulty—ed.) (Continued from page 168)
(...)
But that’s when they are on “The Big Apple,” which is the jockeys’ name for the circuit which includes the big and fashionable tracks — Belmont, Saratoga, Hialeah, Santa Anita, and a few others. The small and more obscure tracks are called “The Merry-Go-Rounds,” and theirs is “The Leaky-Roof Circuit.”
 
Google Books
Fabulous Bawd;
The Story of Saratoga
By Mel Heimer
New York, NY:  Holt
1952
Pg. 13:
They follow the sun to Hialeah and Santa Anita in the winter and up through the Big Apple of the New York tracks in the summer, chasing the buck grimly and doggedly — and then they come for a month to Saratoga and they slow up a little and become, for a moment, the improvers of the breed.
 
Old Fulton New York Post Cards
20 December 1954, The Times Record (Troy, NY), pg. 28, col. 3:
Racing Commission Urges
State To Cut Mutuel ‘Bite
New York (AP)—The State Racing Commission conceded yesterday that Hollywood and Santa Anita in California had succeeded New York tracks as “the big apple” in purse distribution, and again recommended a reduction in the 15 per cent tax take-out in the parimutuel betting.
(...)
Attendance at Belmont, Jamaica, Saratoga and Aqueduct was 4,395,646 and betting totalled $363,306,510.
 
mReplay
Perry Mason - The Case of the Jilted Jockey (television air date: November 15, 1958)
Transcript
(...)
00:30:43 Do you know what a trainer has to do to get a horse like bright magic?
00:30:47 It starts out at the fairs.
00:30:49 $200 Claimers—lame, riddled, wind-broken.
00:30:53 Then you woryourself up, but you don’t find a horse like bright magic.
00:30:58 Oh, no, they don’t run at the half-milers.
00:31:00 You have to sort of graduate—move up to the mile tracks.
00:31:05 Then to the big apple.
00:31:07 Big apple?
00:31:08 Yeah, saratoga, belmont.
00:31:09 You know, the equivalent of santa anita and hollywood park out here.
00:31:14 And then you work and slave and pray and hope that you’ll find a horse like bright magic.