What a great and very helpful thread!
I'm currently re-reading Backstage Pass to Broadway by Susan L. Schulman, a longtime press agent. The chapter about Lesley Ann Warren's behavior on the musical "Dream" is absolutely priceless. The book is very slim (under 200 pages) but filled with wonderful anecdotes about the people Schulman dealt with during her peak years.
I also love Not Since Carrie, The Season by William Goldman, all the Ethan Mordden books, all the Peter Filichia books, The Making of No, No, Nanette and Showtime by Larry Stempel.