You forgot Wards and Randalls Island too.
And City Island, High Island, Coney Island, Mill Island, Hunter Island, Twin Island, Mill Rock Island, U Thant Island, North Brother Island, South Brother Island, Liberty Island, Ellis Island, Shooter's Island, Island of Meadows, Prall's Island, Hoffman Island, Swinburne Island, Berrian's Island, White Island, Barren Island and many others.
And what about Broad Channel?
Now the fact that nearly all of these islands are uninhabited and some of them aren't even islands doesn't matter.