Re: Eastern Long Island
We did Shelter Island a few years ago. 6 foot draft, no issues. But then we stayed at the more remote places, not the harbor up by Greenport.
We picked up a mooring in Sag Harbor for $150 for the night, on that same trip. Watch the chart carefully at Sag and getting into Coecles harbor (really more of a beautiful lake than a harbor). Coecles had a dredged channel that's narrow, but no issues. (I think there's also a rock east of the approach to the channel that locals marked with floating plastic bottles -- at least that's what I guessed it was as I stayed away from it.)