The term has faded into disuse, like many other Broadway nicknames.
http://en.wikipedia.org/wiki/Appian_way
The Appian Way (Latin: Via Appia) was the most important ancient Roman road. Its importance is indicated by its common name, recorded by Statius (Sylvae, 2.2):
"Appia longarum teritur regina viarum"
"the Appian way is commonly said to be the queen of the long roads"
The Romans sensed the inherent nobility of the road imbued by the circumstances and method of its construction, and its utility to the Roman Republic. The via Appia was the paradigm of all subsequent Roman roads. It was the very symbol of the republic, which brought order to the terrain and peace and freedom to the peoples of Italy, at least in their ideals. Their greatest historian, Livy, took that point of view. He was not a Roman by birth.
23 June 1907, Chicago Daily Tribune, "Modern Rural Sports" by "O. Henry," pg. E4:
"I run over to New York every two weeks to see a show," says the farmer, hanging up the receiver. "I catch the eighteen hour flyer at Indianapolis, spend ten hours in the heyday of night on the Yappian way, and get home in time to see the chickens go to roost forty-eight hours later."
28 February 1928, Chicago Daily Tribune, pg. F4:
The Yappian Way.
Broadway is the street of broken hearts.
(...)
---N. J. R. in Life.
13 October 1943, Chicago Daily Tribune, pg. 18:
O. Henry nicknamed New York's Broadway as "the Yappian way," and the same pun has sprung, as an original flash of wit, from the lips of numerous illiterate wisecrackers.

