“The way to a man’s heart is through his stomach” is a classic saying from the early 1800s. “Anybody who believes that the way to a man’s heart is through his stomach flunked geography” is a popular anti-proverb.
 
Robert Byrne included the one-liner in 1,911 Best Things Anybody Ever Said (1988)—one of the few in the book written (and not collected) by Byrne himself.
       
 
Google Books
1,911 Best Things Anybody Ever Said
Edited by Robert Byrne
New York, NY: Fawcett, Columbine
1988
Pg. 326:
281
Anybody who believes that the way to a man’s heart is through his stomach flunked geography.
Robert Byrne
 
23 October 1988, Syracuse (NY) Herald American, “They said it: Author collects one-liners not found in Bartlett’s” by Amy Kantor, pg. AA1, col. 4:
Bryne—in a fit of immodesty—sprinkles a few of his own comic jibes throughout the tome.
(...)
And, “Anybody who believes that the way to a man’s heart is through his stomach flunked geography.”
   
Google News Archive
4 August 1994, The Ledger (Lakeland, FL), “Dear Abby” by Abigail Van Buren, pg. 6C, col. 4:
RANDOM THOUGHTS
“Anyone who thinks the way to a man’s heart is through his stomach must have flunked anatomy.”
ANONYMOUS, BUT IT SOUNDS LIKE WOODY ALLEN
 
20 July 1997, Augusta (GA) Chronicle, “Bachelors have image to uphold” by Bill Kirby, pg. 1C, col. 1:
Anyone who says the way to a man’s heart is through his stomach flunked geography.
 
Google News Archive
8 February 2001, The Times Record/Roane County Reporter (Spencer, WV), pg. 2B, col. 2:
Anybody who believes the way to a man’s heart is through his stomach flunked geography.
     
Google Books
Chicken Soup for the Soul
Healthy Living Series: Heart Disease:
Important Facts, Inspiring Stories
By Jack Canfield, Mark Victor Hansen and Vicki Rackner
New York, NY: Open Road Integrated Media
2013
Pg. ?:
Anybody who believes that the way to a man’s heart is through his stomach flunked geography. —ROBERT BYRNE
   
Twitter
Ian Makay
‏@IanMakay
Anybody who believes that the way to a man’s heart is through his stomach flunked geography. ~Robert Byrne #quote RT @foodiewino712
3:00 PM - 19 Feb 2015