re: habitated (by the living) This struck me as funny! Is there one that's a cemetery, then?
Yes, (see above) Hart's Island is home to NYC potters field. (Potters field--idiom used to define a cemetary for the destituted, from NT-)to get to Hart's island, you take road/bridge to city island,then ferry to hart's island. (there was a movie--with Michael douglas--(i'll never tell..crazy girl keeps repeating) not to long ago, that had city island/ferry to harts island and potters field as 'story element'--i always forget the name of it..)

and another island is habitated by the incarcarated--Riker's Island (a place that is known to watcher of Law & Order) is another east river island. (if you ever fly into NY's LAG airport, the last thing you see before you land is riker's!) is very close to LAG.

Ward's island/Randle's Island- (they used to be 2 islands, but land fill has made them one) is home to a number of state hospitals--it used to house orphanages, and to the city's soccer stadium, and to fire department training buildings. (they keep burning them down!)--

Roosevelt island is best known, but then roosevelt island used to be Blackwell island, and it was there that typhoid mary was keep as public health criminal. back then it didn't have a bridge, subway stop and cable car connection to manhattan or queens. and tides in the east river can run at 20 knots, so the water way is an effective barrier (hell gate, is at the north end of roosevelt is. the worst part of the east river is well named--its full of eddy's and whirlpools.

the brother islands (yes, there are 2 brothers) are bird santuaries, i don't know the name of the island with the lighthouse). the remaining island are all pretty small, and some are demi islands--they are almost submerged at high tide!
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to go clamming, you use a rake (the kind with short, stiff teeth) --actually there is a special clamming rake, but if you don't have one, a garden rake will work-- and you rake the clams out of the sand (muck, really, as much dirt as there is sand) and dump them in a bucket filled with sea water..

better still, is to use something like a laundry basket at first, the sea water washes over/through and help wash out the sand and grit.. and then transfrer to a bucket that holds water to take them home.. and you wear gloves!