It's to the left of the 1 Shubert Alley gift shop, the closest door to the theater.
There are actually two stage doors in the alley (the Shubert and the Booth next door), plus another entrance to the Booth, so make sure you hit the right one.
"Valtava, iso pullean hurmaava HITTI." New York Post (as quoted by Hairspray, Finnish Regional Production.)