There is perhaps no more important island in the world. Those who live there or are familiar with the correct pronunciation of its name say M[ə]nháttan, with a schwa in the first syllable, unlike those who either know the correct pronunciation and choose to ignore it or are simply ignorant of it. (As a former resident of Manhattan [1980-2003], who has recently come back to the borough to live once again, I can report that it grates on my ear every time I hear the word mispronounced.)
In the case of Manhattan, Kansas, or Manhattan Beach, California, naturally, the relevant vowel is not a schwa but the expected [æ].
This case illustrates the possibility that local pronunciations of toponyms may differ from generally more familiar ones. In the USA, think of towns that carry the name Vienna, Cairo, and Berlin but diverge phonetically from their form as designations of foreign cities.