The Starlite, on W. 44th between Broadway and Eighth, is one of the older small businesses to be found on the sidestreets of Times Square. The interior is fairly modern and new, but the sign's stayed the same over the years. No doubt the name, when first conjured, had something to do with the various Broadway attractions in the surrounding area; quaint to think of stage actors as stars these days.
Oh, the opportunities to "Eat-In," as the sign offers, are fairly minimal, unless you like to stand while you lunch. And why "Eat-In" requires a hyphen, while "Take Out" does not, I have no idea. Actually, I think the other way around would make more sense.