There was a rumor in the Soviet Union that The Beatles had secretly visited the U.S.S.R. and given a private concert for the children of top Communist party members. They believed the song "Back In The U.S.S.R." was written because of the concert. Actually, some fans still believe so.
"Piano Man" was inspired by Billy Joel's time playing at a piano bar in Los Angeles. The "real estate novelist" was a guy who always talked about writing a book, but spent all his spare time in the bar.