The Palace Theatre (Broadway between 46th and 47th Streets) opened in 1913 and hosted vaudeville acts until 1932, when it became a movie palace. The Palace Theatre now is home to Broadway shows.
 
To “play the Palace” was the pinnacle of vaudeville success. Performers waited outside the Palace for casting calls; the ‘“panicked” and often unemployed performers called the sidewalks outside the Palace Theatre “Panic Beach.” A nearby traffic island (Duffy Square, the current location of the TKTS tickets booth) was called “Panic Island.” 
 
“Panic Island” is cited in print from at least 1927 and may have been coined by Variety. Jimmy Cagney—recalling his hard-luck acting days from 1920-1925—used “Panic Beach” in a 1956 interview and a 1976 autobiography. The terms are of historical interest today.
 
“Panic Beach/Island” has also been called “Palace Beach” (or “The Beach”) and “Hope Island.”
 
   
Wikipedia: Palace Theatre (Broadway)
The Palace Theatre is a legitimate Broadway theatre located at 1564 Broadway (at 46th) in midtown-Manhattan.
 
History
Designed by architects Kirchoff & Rose, the theatre was built by Martin Beck a California vaudeville entrepreneur and Broadway impresario. The project experienced a number of business problems before it opened. E. F. Albee, one of the main executives for B. F. Keith and his powerful vaudeville circuit, demanded that Beck turn over three-quarters of the stock in the theatre in order to use acts from the Keith circuit. In addition, Oscar Hammerstein was the only person who could offer Keith acts in that section of Broadway, so Beck paid him off with $225,000. The theatre finally opened on March 24, 1913 with headliner Ed Wynn. To “play the Palace” meant that an entertainer had reached the pinnacle of his career, and it became a popular venue with performers like Sarah Bernhardt, Eddie Cantor, Bob Hope, Fanny Brice, Sophie Tucker, George Jessel, and Jack Benny.
 
With the Great Depression came a rise in the popularity of film and radio, and vaudeville began its decline. In 1929 the two-a-day Palace shows were increased to three. By 1932, the Palace moved to four shows a day and lowered its admission price. In November of that year, it converted to a movie house. Appearing on the closing bill when the venue ended its stage policy were Nick Lucas and Hal Leroy. There was a brief return to a live revue format in 1936, when Broadway producer Nils T. Granlund staged a series of variety shows beginning with “Broadway Heat Wave” featuring female orchestra leader Rita Rio. Citizen Kane had its world premiere at the theatre on May 1, 1941.
 
10 August 1927, Variety, pg. 31, col. 2:
‘Panic Island’ in Square
“Panic Island” is the favorite summer sojourning place of vodvil actors compelled to remain in New York. This island is located opposite the Palace theatre building in New York. It is a triangular strip of land dividing Broadway from 7th avenue between 46th and 47th streets.
 
Recently an out of town manager asked an actor where he could be found when wanted. The actor pointed his finger in the direction of the park and explained “over there, on Panic Island.”
   
25 August 1927, Bismarck (ND) Tribune, “In New York” by Gilbert Swan, pg. 4, col. 6:
There are a couple of dozen such born every few minutes at a triangle formed on Seventh Avenue by the interjection of 46th and 47th Streets, which “Variety” refers to as “Panic Island.”
 
This is the spot where gather those vaudevillians forced by business and necessity to stay in town during the summer months. Here out-of-town managers coming to Broadway to engage “numbers” can find almost any sort of act and actor they wish.
 
11 June 1930, Billings (MT) Gazette, “A New Yorker At Large” by Deming Seymour, pg. 11, col. 1:
The actor’s jungle is around Panic Island in Times Square, and a block up Broadway is where musicians rally.
 
26 May 1932, Sandusky (OH) Register, “New Yorker’s Daybook” by Mark Barron, pg. 4, col. 2:
ON “PANIC ISLAND”
On the Bowery are bread lines and broken down men. Well, in the heart of Broadway is a block-wide subway grating known as “Panic Island.” It got its name because when actors have no bookings they say “the panic is on,” and scores of unemployed actors use “Panic Island” as a loafing spot.
 
Each night on “Panic Island” there gathers a bread line of broken men much larger than any you could see on the Bowery.
 
7 December 1936, Denton (TX) Record-Chronicle, “Man About Manhattan” by George Tucker, pg. 2, col. 2:
That large safety zone in Times Square is “Panic Island.”
     
31 December 1956, Bradford (PA) Era, “Behind the Scenes in Hollywood” by Harrison Carroll, pg. 10, col. 8:
“In your early New York stage days,” I ask, “was there any place like this extra’s pull-pen?”
 
“Yeah,” says Jimmy (James Cagney—ed.), “on Forty-Seventh street, near Duffy’s square, there was an area called Panic beach or Panic island. Out-of-work actors used to gather there after making the rounds of the managers’ offices.”
 
“Were you ever one of them?” I inquire.
 
“I sure was,” he laughs. “From 1920 to 1925, I spent plenty of time on Panic beach.”
 
17 March 1974, Las Cruces (NM) Sun-News, “Cagney Lives Up To Advances” by Vernon Scott, pg. 18, col. 7:
“I was broke and looking for work a lot in the old days,” he (James Cagney—ed.) went on. “I used to hang around Panic Beach at the corner of 47th Street and 7th Avenue. All the unemployed hoofers stood around comparing notes, hoping somebody would come along and hire them.”
 
Google Books
Cagney by Cagney
By James Cagney
Garden City, NY: Doubleday
1976
Pg. 29:
There I was, ham-and-egging it around New York, standing on the Forty-seventh Street corner we vaudevillians called Panic Beach, listening to all the theatrical gossip and rumos of jobs surfacing here and htere.
 
Google Books
The City in Slang:
New York Life and Popular Speech
By Irving Lewis Allen
New York, NY: Oxford University Press
1993
Pg. 61:
People in show business also called the blocks of Broadway through Times Square The Street, representing the concentration of their industry. For young hopefuls, however, The Street was 47th Street between Sixth and Seventh Avenues—Dream Street, as Damon Runyon named it. Just off Broadway, this was the block with the offices and stagedoor of the B. F. Keith’s Palace Theater, the mecca of American vaudeville from its opening in (Pg. 62—ed.)  1913 until it became a movie house in 1932. Panic Beach was the sidewalk in front of the Palace and was so named for the unemployed performers who waited and milled about there.