Re: Eastern Long Island
Just spend 3 days at Coecles Harbor Marina (mooring rental $48/night for my Catalina 320 - $1.50/ft). Nice place! Beautiful, quiet. They have a nice pool, rent bikes and will shuttle you to town/ferry. They even rent electric cars!
Channel is shallow, but they provide navigiation tips on their website. We draw 4'10" and had no issues - Sounds like you it could be a challenge with a draft of 6'5", but you could give them a call.
Years back we spent time in Dering Harbor, on the other side of Coecles. Deeper water, but much more crowded mooring field - and services aren't as good, unless you are reciprical with SIYC. Same trip spent two days at Three Mile Harbor - Nice spot, but long walk into East Hampton.
Oh, and Rams Head Inn is no longer in business.
If you head this way, enjoy! It's a beautiful area to sail - just pay attention to tides/currents in and out of Gardiners Bay!