If someone jumps in your cab in Manhattan and requests Roosevelt Island, simply drive up Third Avenue (or down Second Ave) and over the upper level of the Queensboro Bridge.
Take the 21 Street exit (fork right) and make a right unto 21st Street, which goes under the bridge. Drive past the Queensbridge Housing Project on the left and make a left unto 36 Avenue.
Follow that straight over the little draw bridge that brings you into Roosevelt Island. There is only one way in and one way out by car.
Upon dropping off, what I like to do is go back down 21st Street, but instead of getting back on the bridge to Manhattan, I continue through the heart of Long Island City and make a right unto Jackson Avenue, or cut over to PS 1 and Courthouse Square. Sometimes there'll be a fare there. Otherwise, it's over the Pulaski Bridge into Greenpoint. Down McGuinness.
Perhaps a right on Greenpoint Ave. and a left on Manhattan Avenue, or a quick loop around the bars on Franklin. On Driggs by McCarren Park there are some bars two. If all of that yields no passengers, go down Driggs through Williamsburg and up Bedford Ave. and down Wythe Street and back up Bedford again, from down by the Willie Bridge. If none of this works, head down Metropolitan to Union or Lorimer. Something's gotta give in these parts!