A Big Apple Cafe existed at 1112 First Street West in Calgary, Alberta, Canada, from 1938 until 1940. The Big Apple Cafe was almost surely named after the “Big Apple” dance craze of 1937, just one year before.
 
 
Newspapers.com
20 February 1939, Calgary (Alberta) Herald, pg. 10, col. 7:
A brown leather purse, containing about $3, was stolen Sunday afternoon from Mrs. A. Morrison, in the Big Apple Cafe, 1112 First street west.
   
Newspapers.com
26 April 1939, The Albertan (Calgary, Alberta), pg. 13, col. 1 ad:
FREE
COFFEE
TODAY
To Celebrate Our
FIRST ANNIVERSARY
(...)
The Big Apple Cafe
1112 First Street West
 
Newspapers.com
25 November 1939, Calgary (Alberta) Herald, pg. 9, col. 5 ad:
BIG APPLE CAFE
HOME COOKED MEALS
BY ANN MORRISON
ROAST CHICKEN, with Dressing ... 35 c
1112 FIRST STREET WEST
2 doors south of Isis Theatre M4929
 
Newspapers.com
6 February 1940, Calgary (Alberta) Herald, pg. 9, col. 1 ad:
BIG APPLE CAFE
The Home of the Home-Cooked Meals
SMALL STEAK 25c
1112 First Street West—M4929
 
Newspapers.com
27 February 1940, Calgary (Alberta) Herald, pg. 9, col. 7 ad:
BIG APPLE CAFE
THE HOME OF THE HOME-
COOKED MEALS
1112 First Street West—M4929