Mark Steyn, as usual, hits the nail on the head by calling Leonard Bernstein's music "spikey...and tragic."
And the one contemporaneously cool term they deployed - "Cool" - was transformed by Bernstein and his lyricist, Stephen Sondheim, into something with a rare kind of Broadway cool all its own:
Bernstein's score nods towards some of the rhythms of the day - the mambos and cha-chas - but it never sounds like Fifties pop tunes, just unmistakably Bernstein: spikey, finger-snappy, urban ...and tragic.
West Side Story was a regurgitation of Shakespeare's "Romeo and Juliet" with the Sharks and Jets taking over the role of the Montegues and the Capulets. But the movie is timeless and always a good time. As a police officer the part with "Officer Krumpke" is classic. As the cop mouths off to the "delinquents" - the gang members roll off a litany of rationalizations to excuse their horrific behavior.
More here at wikipedia.