Hi,
Claudios offers docking ;-) , just kidding.
Also, very close is the Shelter Island town dock in Derring harbor. Free tie up and you can walk to restaurants in the heights.
On shelter on the south side is the island boatyard, they allow docking for diners at the restaurant there.
You can also anchor off crescent beach and take a launch (was $10 per person each way last year, we declined the $80 round trip to go 100 ft. for the 4 of us. )
You can doc at the town slips in Sag and go to restaurants there, you'll need top pay for the dockage by the hour
Orient by the Sea has docking, but , not sure you'd want to bring you large boat into that small basin.
Montauk - Ricks Crabby Cowboy has docking for diners. Not sure of the fees, but, you can dock at the Montauk Yacht club and dine. I would think Star island too. As far as I know there is no docking in fort pond, but, if you have a dink you can anchor and dingy in to navy beach
Abbott's Lobster in Noank, CT