"Where the East ends” is the Dallas response to Fort Worth’s slogan “Where the West begins.” The Dallas slogan is usually not used by itself, without Fort Worth’s slogan.

Other Dallas slogans include “Live Large, Think Big” (since 2004) and “Big Things Happen Here” (since 2012).


23 February 1932, Dallas Morning News, “Regional Planning,” section II, pg. 2: 
A carefully planned metropolitan system, combined with a larger regional plan, will bring into an orderly union the city where the west begins and the city where the east ends, making the joint city the center of industrial and commercial energy. 

Google Books
Inside U.S.A.
by John Gunther
New York: Harper & Brothers
1947
Pg. 830:
Dallas is where the east ends, and Fort Worth is notoriously “where the west begins.” Dallas is a baby Manhattan; Fort Worth is a cattle annex. Dallas has the suave and glittering clothes of Neiman-Marcus; Fort Worth has dust and stockyards.

11 May 1951, Dallas Morning News, part II, pg. 8:
Then there is Fort Worth “where the West begins” dating with the arrival of Amon Carter. Dallas is also Texas and Dallas is “where the East ends.”

Google Books
Lone-Star Land:
Twentieth-Century Texas in Perspective
by Frank Goodwyn
New York: Knopf
1955
Pg. 225:
While Dallas might be called “out where the east ends,” Fort Worth has long vaunted the slogan: “out where the west begins.”

James C. Work’s Amazon Blog
Who Are You Calling “Western”?
7:17 AM PDT, August 7, 2007
(...)
I once saw a sign in Fort Worth, Texas. It said “where the West begins.” And on the backside, some wag had added “where the East ends.”