I don't recall any individual islands on Staten Island... you may be thinking of surrounding islands that are on the bay, such as Governor's Island, Ellis Island, Liberty Island...
I think the landfill is somewhat likely, as it is one place where tools may not have been necessary to conceal a body. A few larger pieces of garbage may have done the trick, and an odor may not be detected because that place always smelled awful... as much as I hate the thought...
This makes sense to me, especially in light of the recent death of a woman who was found by the smell of decomposition in one of the parks. I wonder, though, if it was easy to enter the landfill? I wouldn't think just anyone could get in there-maybe back in the 70's you could?