Edited to add that Eddie Fisher was an entertainer who perpetuated this story. In his autobiography, Fisher said (notice he said 'supposedly' about the sign) ...
One of the best-known anti-Semites in show business was Arthur Godfrey, the host of radio's most important amateur talent contest. Godfrey owned the Kenilworth Hotel in Florida, which supposedly (sic) had a sign in front that read NO DOGS OR JEWS ALLOWED. But when I got the opportunity to appear on Talent Scouts, I leaped at it. I didn't care that Godfrey wouldn't let me in his hotel as long as he let me sing on his radio show.
However author Arthur Singer points out that Godfrey had no financial stake in the Kenilworth at the time Fisher appeared on Talent Scouts.
Arthur J. Singer, author of Arthur Godfrey: The Adventures of an American Broadcaster (2000), rejects this accusation, citing Godfrey's good personal relations with a number of Jews in the entertainment industry, including his longtime announcer Tony Marvin. As for Godfrey's association with the Kenilworth, the hotel did establish a "No Jews" policy in the 1920s, but abandoned it when Godfrey acquired a stake in the hotel in the early 1950s. In the eyes of the public, the increasingly negative, and largely self-inflicted publicity Godfrey, despite his ongoing popularity, had generated since 1953 no doubt added credence to the accusations. In fact Godfrey was only a part-owner of the hotel and insisted that when he took that stake, he ended any discriminatory policies that existed. Further undermining Fisher's account, he appeared on Talent Scouts years before Godfrey purchased a part interest in the Kenilworth.
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