You might want to also check out the 79th at boat basin in NYC
, they have transient slips and moorings, and its not expensive. And its on Manhattan island. A little detour since to go to LI Sound you will have to go back down the Hudson
a few miles to round the battery
and go back up the east river through hell gate. Don't know if anyone mentioned here but there are really only a few hours each tide cycle when you can go through there so read up and plan accordingly.
As far as detours though, if you did stay at 79th st and went up even further say to Tarrytown, Nyack or Croton point, its very beautiful up there in the summer. This is prime territory of the Hudson
of landscape painters of the 1800s. Nyack has moorings tarrytown has slips, and there is a nice big shallow area that's good to anchor
for free just north of croton point. Prob would add 1 day to your trip for the detour. Go on a nice sunny day. Work the tides.