1) all of them. NYU, Sinai, Columbia, Cornell, Einstein, Downstate, NYMC, NYCOM all have presence in the 5 boroughs proper. Stretch a little outside of the 5 boroughs and you add Stony Brook and Touro.
2) Bronx: Morrisania, Highbridge, Hunts Point, Ferry Point, Mott Haven, Union Port, Burnside, Pelham, Bedford Park, Hudson, Bathgate, Williamsbridge, Edenwald
Brooklyn: Crown Heights, Bed-Stuy, Some areas of Borough Park
New York County: Clinton (odd. I live there. Its a nice part of midtown), East Harlem, Central Harlem, Inwood/Washington Heights
Queens: South Jamaica, North Central Corona, Northwest Queens,
Staten Island: None
This isn't all inclusive, but you can look these places up and a large majority of the places aren't "communities" that are medically underserved, but rather really tiny areas. So hospitals wouldn't serve them, individual offices would have to. I listed the communties and skipped all of the "brooklyn between 3rd ave and 5th ave and 71st street and 78th street." Which is not really medically underserved "area" then, it just happens to be an area that is mathematically too far away from any hospital so it falls into the search net.
http://muafind.hrsa.gov/