
Originally named International Music Hall, the "names 'Radio City' and 'Radio City Music Hall' derive from one of the complex's first tenants, the Radio Corporation of America" (RCA) (source: Wikipedia). You can read more about its history here on the Radio City Music Hall website.
Although Radio City is only 90 minutes away, I have only been there twice. First time was in 1962, when Aunts Nellie and Stephanie took my sister Jeanette and I to see the live show (the Rockettes and all) and a film (Rome Adventure). The second time was in 1991, when my wife Laurie, daughter Hayley, and sister (still Jeanette) attended the Christmas live show (the Rockettes and all), but no film. Between 1962 and 1991, they jettisoned the film, but increased the admission price!
And so it goes.