A busy author for the screen and the stage , Mr. Davis wrote 15 movies and dozens of scripts for television series , and he had a hand in five Broadway shows , including writing a 1945 play , " Kiss Them for Me , " about four sailors back from the war , and the book for " Grand Hotel , " the musical adaptation of Vicki Baum 's novel , which was directed and choreographed by Tommy Tune and which ran for more than 1,000 performances from 1989 to 1992 .