Personally, I think my dandruff is caused by a history of eczema, shitty New York tap water, and chronic bad juju. After my traumatic episode, I searched the racks of Duane Reade for any type of drugstore-brand scalp treatment, when I came across a familiar face: tea tree oil.
From Midtown or the Village, take the F or D trains that run down Sixth Avenue from Central Park to Washington Square or the N or Q trains that run down Broadway to Canal Street. All four of these trains will take you directly to Coney Island in Brooklyn.
There is train service into Manhattan, and then a subway connection, from EWR. I'm not sure you can easily do public transit from LGA, though you could from JFK (free bus to Howard Beach Station, and then subway ride...would be about an hour trip once you're on the subway).