If Broadway, as it is generally referred to, is a neighborhood in NYC known for it's theaters, in spite of the fact that most of the theaters are not located on Broadway itself, and in spite of the fact that the street named Broadway extends the length of Manhattan, so that even if you're on Broadway you might not be in the area known as Broadway...
Then it is logical that "West End Avenue" also refers to a neighborhood, in spite of the fact that not everything in that nieghborhood is on West End Avenue itself, and that the Avenue extends beyond the neighborhood referred to.
Therefor, when Stephen Schwartz wrote the lyric line "Delis and laundromats and gay bars" in 1974, he was being accurate. Most people would have understood what he was writing.
Besides, it's the universality of the song, the conundrum of wanting to leave home yet finding oneself unable to leave, that Schwartz was writing about. His use of specifics, such as "And you subway to school with kids whose folks all live in twenty blocks/ In a high-rise rented carton or a co-op brownstone box," is easy for listeners to relate to, in spite of the fact that most students don't ride to school on subways, or live in a brownstone. I always walked to school; the grandlads ride on a yellow school bus. They live in a two-story house in the woods; I grew up in a single-family house in what was then considered a suburb, or at least a "bedroom community." All the same, the monotony of life growing up anywhere, the desire to break out of that monotony, and the irritating knowledge that "home" would be waiting for me, these things were all identifiable as part of life. This is what Schwartz was writing about, and in a very real way what he wrote was comforting to me, as he helped me recognize that I wasn't alone, that people leading very different lives than mine on the outside could be leading the same life as mine on the inside.
The song is quite accurate.
(Edited for punctuation. Dash it all.)